Which of the given differential equations are linear and to determine the order of each equation.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 9, Problem 1CRE

To determine

Which of the given differential equations are linear and to determine the order of each equation.

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

(b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Explanation of Solution

Initially check for linearity. Then observe the higher order derivative to determine the order of the equation.

Given:

(a) $y' = y^{5} - 3 x^{4} y$

(b) $y' = x^{5} - 3 x^{4} y$

(c) $y = y''' - 3 x \sqrt{y}$

(d) $\sin x . y'' = y - 1$

Calculation:

(a) $y' = y^{5} - 3 x^{4} y$ - $y^{5}$ is a non-linear term, hence this is not a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(b) $y' = x^{5} - 3 x^{4} y$ - this is a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(c) $y = y''' - 3 x \sqrt{y}$ - $\sqrt{y}$ is a non-linear term so this is not a linear equation. This is a third order equation as the third derivative is the highest order derivative here.

(d) $\sin x . y'' = y - 1$ - this is a linear equation. This is a second order equation as the second derivative is the highest order derivative here.

Conclusion:

Hence, (b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

RK 119 43 Previous Problem University at Buffalo Problem List Next Problem Match the surfaces (a) - (f) below with the contour diagrams (1) - (6) below those. (a) Surface (a) matches contour 5 V V (b) Surface (b) matches contour 2 V (c) Surface (c) matches contour 1 (d) Surface (d) matches contour 6 V (e) Surface (e) matches contour 4 V (f) Surface (f) matches contour 3 V (4) (1) -0.25 (a) (b) (c) (d) (e) y y 2.5 0.5 1.5 1.5 1.5 y .3 0.25 OC 0.25 -0.25 (2) X 1.5 ZI (f) y 0.01 0.01 (3) ☑ X 0.01 0.01 0.2 0.2 (5) 0 x 0.5 (6) 0.25 X X 0.25 0.5

43 University at Buffalo Previous Problem Problem List Next Problem At least one of the answers above is NOT correct. The figure shows a hill with two paths, A and B. (a) What is the elevation change along each path? 400 9400 ✓ feet (b) Which path ascends more rapidly? A v (c) On which path will you probably have a better view of the surrounding countryside (assuming that trees do not block your view)? A V (d) Along which path is there more likely to be a stream? A V Note: You can earn 50% partial credit for 2-3 correct answers. Preview My Answers Submit Answers Q hulu )))) 9800' A 10000 (Click on graph to enlarge) L ^ B 0 Logged in as Luella Ya 4)

find the general soultion (D-DxDy-2Dx)Z = sin(3x+4y) + x²y

Answer 2

Question

Chapter 9, Problem 1CRE

To determine

Which of the given differential equations are linear and to determine the order of each equation.

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

(b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Explanation of Solution

Initially check for linearity. Then observe the higher order derivative to determine the order of the equation.

Given:

(a) $y' = y^{5} - 3 x^{4} y$

(b) $y' = x^{5} - 3 x^{4} y$

(c) $y = y''' - 3 x \sqrt{y}$

(d) $\sin x . y'' = y - 1$

Calculation:

(a) $y' = y^{5} - 3 x^{4} y$ - $y^{5}$ is a non-linear term, hence this is not a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(b) $y' = x^{5} - 3 x^{4} y$ - this is a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(c) $y = y''' - 3 x \sqrt{y}$ - $\sqrt{y}$ is a non-linear term so this is not a linear equation. This is a third order equation as the third derivative is the highest order derivative here.

(d) $\sin x . y'' = y - 1$ - this is a linear equation. This is a second order equation as the second derivative is the highest order derivative here.

Conclusion:

Hence, (b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 9, Problem 1CRE

To determine

Which of the given differential equations are linear and to determine the order of each equation.

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

(b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Explanation of Solution

Initially check for linearity. Then observe the higher order derivative to determine the order of the equation.

Given:

(a) $y' = y^{5} - 3 x^{4} y$

(b) $y' = x^{5} - 3 x^{4} y$

(c) $y = y''' - 3 x \sqrt{y}$

(d) $\sin x . y'' = y - 1$

Calculation:

(a) $y' = y^{5} - 3 x^{4} y$ - $y^{5}$ is a non-linear term, hence this is not a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(b) $y' = x^{5} - 3 x^{4} y$ - this is a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(c) $y = y''' - 3 x \sqrt{y}$ - $\sqrt{y}$ is a non-linear term so this is not a linear equation. This is a third order equation as the third derivative is the highest order derivative here.

(d) $\sin x . y'' = y - 1$ - this is a linear equation. This is a second order equation as the second derivative is the highest order derivative here.

Conclusion:

Hence, (b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 9, Problem 1CRE

To determine

Which of the given differential equations are linear and to determine the order of each equation.

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

(b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Explanation of Solution

Initially check for linearity. Then observe the higher order derivative to determine the order of the equation.

Given:

(a) $y' = y^{5} - 3 x^{4} y$

(b) $y' = x^{5} - 3 x^{4} y$

(c) $y = y''' - 3 x \sqrt{y}$

(d) $\sin x . y'' = y - 1$

Calculation:

(a) $y' = y^{5} - 3 x^{4} y$ - $y^{5}$ is a non-linear term, hence this is not a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(b) $y' = x^{5} - 3 x^{4} y$ - this is a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(c) $y = y''' - 3 x \sqrt{y}$ - $\sqrt{y}$ is a non-linear term so this is not a linear equation. This is a third order equation as the third derivative is the highest order derivative here.

(d) $\sin x . y'' = y - 1$ - this is a linear equation. This is a second order equation as the second derivative is the highest order derivative here.

Conclusion:

Hence, (b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 9, Problem 1CRE

To determine

Which of the given differential equations are linear and to determine the order of each equation.

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

(b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Explanation of Solution

Initially check for linearity. Then observe the higher order derivative to determine the order of the equation.

Given:

(a) $y' = y^{5} - 3 x^{4} y$

(b) $y' = x^{5} - 3 x^{4} y$

(c) $y = y''' - 3 x \sqrt{y}$

(d) $\sin x . y'' = y - 1$

Calculation:

(a) $y' = y^{5} - 3 x^{4} y$ - $y^{5}$ is a non-linear term, hence this is not a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(b) $y' = x^{5} - 3 x^{4} y$ - this is a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(c) $y = y''' - 3 x \sqrt{y}$ - $\sqrt{y}$ is a non-linear term so this is not a linear equation. This is a third order equation as the third derivative is the highest order derivative here.

(d) $\sin x . y'' = y - 1$ - this is a linear equation. This is a second order equation as the second derivative is the highest order derivative here.

Conclusion:

Hence, (b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Answer 6

Chapter 9, Problem 1CRE

To determine

Which of the given differential equations are linear and to determine the order of each equation.

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

(b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Explanation of Solution

Initially check for linearity. Then observe the higher order derivative to determine the order of the equation.

Given:

(a) $y' = y^{5} - 3 x^{4} y$

(b) $y' = x^{5} - 3 x^{4} y$

(c) $y = y''' - 3 x \sqrt{y}$

(d) $\sin x . y'' = y - 1$

Calculation:

(a) $y' = y^{5} - 3 x^{4} y$ - $y^{5}$ is a non-linear term, hence this is not a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(b) $y' = x^{5} - 3 x^{4} y$ - this is a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(c) $y = y''' - 3 x \sqrt{y}$ - $\sqrt{y}$ is a non-linear term so this is not a linear equation. This is a third order equation as the third derivative is the highest order derivative here.

(d) $\sin x . y'' = y - 1$ - this is a linear equation. This is a second order equation as the second derivative is the highest order derivative here.

Conclusion:

Hence, (b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Answer 7

Chapter 9, Problem 1CRE

To determine

Which of the given differential equations are linear and to determine the order of each equation.

Answer 8

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

(b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Initially check for linearity. Then observe the higher order derivative to determine the order of the equation.

Given:

(a) $y' = y^{5} - 3 x^{4} y$

(b) $y' = x^{5} - 3 x^{4} y$

(c) $y = y''' - 3 x \sqrt{y}$

(d) $\sin x . y'' = y - 1$

Calculation:

(a) $y' = y^{5} - 3 x^{4} y$ - $y^{5}$ is a non-linear term, hence this is not a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(b) $y' = x^{5} - 3 x^{4} y$ - this is a linear equation. This is a first order equation as the first derivative is the highest order derivative here.

(c) $y = y''' - 3 x \sqrt{y}$ - $\sqrt{y}$ is a non-linear term so this is not a linear equation. This is a third order equation as the third derivative is the highest order derivative here.

(d) $\sin x . y'' = y - 1$ - this is a linear equation. This is a second order equation as the second derivative is the highest order derivative here.

Conclusion:

Hence, (b) and (d) are linear equations with first and second order respectively while (a) and (c) are non-linear equations with first and third order respectively.

Answer 12

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 4PQ Ch. 9.1 - Prob. 5PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E

Which of the given differential equations are linear and to determine the order of each equation.

Which of the given differential equations are linear and to determine the order of each equation.

Answer to Problem 1CRE

Explanation of Solution

Want to see more full solutions like this?

Chapter 9 Solutions