Program Description: Purpose ofproblem is to calculate the general solution of the differential equation x 3 + 3 y − x y ′ = 0 .

Question

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Answer 1

Question

Chapter 1, Problem 1RP

Program Plan Intro

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation $x3+3y−xy′=0$ .

Expert Solution & Answer

Explanation of Solution

Given information:

The differential equation is $x3+3y−xy′=0$ .

Explanation:

The given differential equation can be written as,

$xdydx−3y=x3dydx−3xy=x3xdydx−3xy=x2$

The above equation is a linear first order differential equation and its solution is calculated as,

$ye−3∫ 1 x dx=∫ x 2 e − ∫ 3 x dx dxye−3lnx=∫ x 2 e −3lnxdxyelnx −3=∫ x 2 e ln x −3 dxyx−3=∫ x 2 x −3dx$

Simplify the above equation.

$yx−3=∫ 1 xdxyx−3=C+lnxy=x3(C+lnx)$

Conclusion:

Thus, the solution of the differential equation $x3+3y−xy′=0$ is $y=x3(C+lnx)$ .

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Answer 2

Question

Chapter 1, Problem 1RP

Program Plan Intro

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation $x3+3y−xy′=0$ .

Expert Solution & Answer

Explanation of Solution

Given information:

The differential equation is $x3+3y−xy′=0$ .

Explanation:

The given differential equation can be written as,

$xdydx−3y=x3dydx−3xy=x3xdydx−3xy=x2$

The above equation is a linear first order differential equation and its solution is calculated as,

$ye−3∫ 1 x dx=∫ x 2 e − ∫ 3 x dx dxye−3lnx=∫ x 2 e −3lnxdxyelnx −3=∫ x 2 e ln x −3 dxyx−3=∫ x 2 x −3dx$

Simplify the above equation.

$yx−3=∫ 1 xdxyx−3=C+lnxy=x3(C+lnx)$

Conclusion:

Thus, the solution of the differential equation $x3+3y−xy′=0$ is $y=x3(C+lnx)$ .

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Answer 3

Question

Chapter 1, Problem 1RP

Program Plan Intro

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation $x3+3y−xy′=0$ .

Expert Solution & Answer

Explanation of Solution

Given information:

The differential equation is $x3+3y−xy′=0$ .

Explanation:

The given differential equation can be written as,

$xdydx−3y=x3dydx−3xy=x3xdydx−3xy=x2$

The above equation is a linear first order differential equation and its solution is calculated as,

$ye−3∫ 1 x dx=∫ x 2 e − ∫ 3 x dx dxye−3lnx=∫ x 2 e −3lnxdxyelnx −3=∫ x 2 e ln x −3 dxyx−3=∫ x 2 x −3dx$

Simplify the above equation.

$yx−3=∫ 1 xdxyx−3=C+lnxy=x3(C+lnx)$

Conclusion:

Thus, the solution of the differential equation $x3+3y−xy′=0$ is $y=x3(C+lnx)$ .

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Answer 4

Question

Chapter 1, Problem 1RP

Program Plan Intro

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation $x3+3y−xy′=0$ .

Expert Solution & Answer

Explanation of Solution

Given information:

The differential equation is $x3+3y−xy′=0$ .

Explanation:

The given differential equation can be written as,

$xdydx−3y=x3dydx−3xy=x3xdydx−3xy=x2$

The above equation is a linear first order differential equation and its solution is calculated as,

$ye−3∫ 1 x dx=∫ x 2 e − ∫ 3 x dx dxye−3lnx=∫ x 2 e −3lnxdxyelnx −3=∫ x 2 e ln x −3 dxyx−3=∫ x 2 x −3dx$

Simplify the above equation.

$yx−3=∫ 1 xdxyx−3=C+lnxy=x3(C+lnx)$

Conclusion:

Thus, the solution of the differential equation $x3+3y−xy′=0$ is $y=x3(C+lnx)$ .

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

Answer 5

Chapter 1, Problem 1RP

Program Plan Intro

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation $x3+3y−xy′=0$ .

Expert Solution & Answer

Explanation of Solution

Given information:

The differential equation is $x3+3y−xy′=0$ .

Explanation:

The given differential equation can be written as,

$xdydx−3y=x3dydx−3xy=x3xdydx−3xy=x2$

The above equation is a linear first order differential equation and its solution is calculated as,

$ye−3∫ 1 x dx=∫ x 2 e − ∫ 3 x dx dxye−3lnx=∫ x 2 e −3lnxdxyelnx −3=∫ x 2 e ln x −3 dxyx−3=∫ x 2 x −3dx$

Simplify the above equation.

$yx−3=∫ 1 xdxyx−3=C+lnxy=x3(C+lnx)$

Conclusion:

Thus, the solution of the differential equation $x3+3y−xy′=0$ is $y=x3(C+lnx)$ .

Answer 6

Chapter 1, Problem 1RP

Program Plan Intro

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation $x3+3y−xy′=0$ .

Expert Solution & Answer

Explanation of Solution

Given information:

The differential equation is $x3+3y−xy′=0$ .

Explanation:

The given differential equation can be written as,

$xdydx−3y=x3dydx−3xy=x3xdydx−3xy=x2$

The above equation is a linear first order differential equation and its solution is calculated as,

$ye−3∫ 1 x dx=∫ x 2 e − ∫ 3 x dx dxye−3lnx=∫ x 2 e −3lnxdxyelnx −3=∫ x 2 e ln x −3 dxyx−3=∫ x 2 x −3dx$

Simplify the above equation.

$yx−3=∫ 1 xdxyx−3=C+lnxy=x3(C+lnx)$

Conclusion:

Thus, the solution of the differential equation $x3+3y−xy′=0$ is $y=x3(C+lnx)$ .

Answer 7

Chapter 1, Problem 1RP

Program Plan Intro

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation $x3+3y−xy′=0$ .

Answer 8

Expert Solution & Answer

Explanation of Solution

Given information:

The differential equation is $x3+3y−xy′=0$ .

Explanation:

The given differential equation can be written as,

$xdydx−3y=x3dydx−3xy=x3xdydx−3xy=x2$

The above equation is a linear first order differential equation and its solution is calculated as,

$ye−3∫ 1 x dx=∫ x 2 e − ∫ 3 x dx dxye−3lnx=∫ x 2 e −3lnxdxyelnx −3=∫ x 2 e ln x −3 dxyx−3=∫ x 2 x −3dx$

Simplify the above equation.

$yx−3=∫ 1 xdxyx−3=C+lnxy=x3(C+lnx)$

Conclusion:

Thus, the solution of the differential equation $x3+3y−xy′=0$ is $y=x3(C+lnx)$ .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation x 3 + 3 y − x y ′ = 0 .

Concept explainers

Program Description: Purpose ofproblem is to calculate the general solution of the differential equation $x3+3y−xy′=0$ .

Explanation of Solution

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Chapter 1 Solutions