The functions y1(t) =t² and y2(t)= t° are solutions of the homogeneous differential equation t?y" – 4ty' + 6y = 0 on (0, 00). When using variation of parameters with y = u1(t)t² +u2(t)t³ to find a solution of the nonhomogeneous lifferential equation t'y" – 4ty' + 6y = 4t³, | vhat is the function u, (t) ? (1) 4 (2) –4 4 (3) (4) t2 (5) –4t (6) –4t?

The functions y1(t) =t² and y2(t)= t° are solutions of the homogeneous differential equation t?y" – 4ty' + 6y = 0 on (0, 00). When using variation of parameters with y = u1(t)t² +u2(t)t³ to find a solution of the nonhomogeneous lifferential equation t'y" – 4ty' + 6y = 4t³, | vhat is the function u, (t) ? (1) 4 (2) –4 4 (3) (4) t2 (5) –4t (6) –4t?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: State the order of the given ordinary differential equation. cosh(4/y) - 5ln(18y)y" = 2cos(5yx) -…

A: Given: cosh(4/y)-5ln(18y)y''=2cos(5yx)-y12y'+4x To find: Order of the given ordinary differential…

Q: Which of the following differential equation has a solution of y = e"(c, cos 2x + c, sin 2x) ? y" –…

Q: Consider the differential equation 3y" +y-2y = 2 cos t Which of the following is the general…

Q: The functions fi(x) 3x and f2(x) 3x-3 %3D %3D form a fundamental set of solutions of the…

Q: Transform the following Bernoulli differential equation of the form 2+ P(x) · y = dx Q(x)y" or +…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: The function y = t² is the solution to the differential equation t²y" — t(t+4)y' + 2(t+3)y = 0. - 19…

Q: The functions y1(t)=t2 and y2(t)=t3 are solutions of the homogeneous differential equation t2y'' -…

A: See the solution in the given fig.1

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

Q: The functions y1(t) = t² and y2(t) = t³ are solutions of the homogeneous differential equation t’y"…

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Introduction: The variation of parameter is a very efficient tool that is used to determine the…

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: We have to find the homogeneous linear differential equation with constant coefficients whose…

Q: (c) and Y2(t) 7. The functions Y₁(t) = t and Y₂(t) = tet form a fundamental pair of solutions to the…

Q: Consider the linear second-order differential equation (x² – 4)y" + (x + 2)y' – 6y = 0. What are the…

A: This question related to frobenius method

Q: x=5cos(t) y=8sen(t) is a parametric solution of the following ordinary differential equation?

A: Here dy/dt=8cos(t) And dx/dt=-5 sin(t) Divide both and we get dy/dx= (-8/5) cot(t) and from given…

Q: 17. Determine the differential equation whose general solution is y = C,Sin3t + C,Cos3t . d? y - 9y…

A: Topic = Differential equation

Q: (b)2(2y² + 5xy − 2y + 4)dx + x(2x + 2y − 1)dy = 0 Ans. x4(y² + 2xy = y + 2) = c

Q: 3. Given that y₁ = t−¹ is a solution of 2t²y" + 3ty' — y=0, t>0, a) Substitute y = v(t)y₁(t) into…

Q: Determine the solution of the integro-differential equation: Y -9y()+ 10 19sen(-8t) y(u)e* 4t -4u…

A: To solve the below integrodifferential equation. dydt−9yt+10∫0tyue4t−4udu=−19sin−8t2−7cos−8t−e4t,…

Q: 3. Solve the differential equation subject to the given conditions. d² y dx² a) b) d² y dx² +36y= 0,…

A: As you didn't mention the question number to be solved so I solved two questions. For remaining…

Q: y" + 16y = sec(4x). a. Find the most general solution to the associated homogeneous differential…

Q: The suitable form of the differential equation y" + 2y'-3y = 5e2t, is Y = Aje2t, then the value of…

Q: show, by direct substitution, that the given functions y1(t) and y2(t) are solutions of the given…

A: Given differential equation y''+4y=0 y1(t)=cos(2t) , y2(t)=sin(2t)

Q: i) Determine whether the given functions is linearly dependent or linearly independent: y1 = 2x2, y2…

Q: Solve the second order homogeneous differential equation y" -4y + 9y = 0 Select one: O a. e-2" (a…

A: From the given problem: y''-4y'+9y=0 So, we can write as: D2y-4Dy+9y=0D2-4D+9y=0 The…

Q: Find the function y = f(t) passing through the point (0, 10) with the given differential equation.…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The functions yı(t) = t² and y2(t) = t³ are solutions of the homogeneous differential equation
t?y - 4ty + бу — 0 on (0, 0).
on (0, 00).
When using variation of parameters with y = u1(t)t²+u2(t)t³ to find a solution of the nonhomogeneous
differential equation
t?y" – 4ty' + 6y = 4t³,
what is the function u, (t) ?
(1) 4
(2) -4
4
(3)
4
(4)
t2
(5) –4t
(6) –4t2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Find a homogeneous linear differential equation with constant coefficients whose general solution is given. y = C₁ + c₂e5x Oy" + 5y = 0 Oy" + 5y' = 0 y" - 6y' + 5y = 0 Oy" - 5y' = 0. Oy" - 5y = 0 Need Help? X Read It
Consider the differential equation: y"+ 18y + 81y = t ?e-t, t> 0. 2 a. Find the general solution to the corresponding homogeneous equation. In your answer, use c¡ and c2 to denote arbitrary constants. Enter c1 as c1 and c2 as c2. Yc = cle 9t 1+ c2-94 A b. Apply variation of parameters to find a particular solution. Yp 91,-691 log(1) t-e
. Find solution to the following differential equations (а) сos x(e2У -у) dy = e°sin 2x dx (0) = 0 dy _ху + 2y — х — 2 (b) dx ху — Зу + x — 3
Determine the two singular points of the differential equation (x² - 81)y" + (9 − x)y′+ (x² + 18x +81)y = 0 List the points in increasing order: x1 = x2= Which of the following statements correctly describes the behaviour of the solutions of the differential equation near the singular point x1: A. All non-zero solutions are unbounded near 1. B. All solutions remain bounded near x1. C. At least one non-zero solution remains bounded near x1 and at least one solution is unbounded near x1. Which of the following statements correctly describes the behaviour of the solutions of the differential equation near the singular point 2: O A. All solutions remain bounded near 2. B. At least one non-zero solution remains bounded near 2 and at least one solution is unbounded near x2. C. All non-zero solutions are unbounded near 2.
Let u₁ and u2 be two linearly independent solutions of the second-order linear differential equation (i) (ii) d² u fu dx² 2 + - 0, f = f(x). Let w = uz/u₁. Show that w' = c/u for some nonzero constant c. Let y = -2u₁/u₁. Show that y satisfies the Ricatti equation y² V-2-1 y' f.
y = A sin(kt) is a solution of the differential equation y'' + 16y = 0, a value of K is: a) 2 b) 3 c) 4 d) 1