Answer the following questions 4.Find the explicit result for function y (i.e. function y = an function in term of x) of the initial valueproblem3xy=-y(0) = -4 .y+x*y'Verify that (e* sin y+3y)-(3x - e* sin y)y' = 0 is exact.Then solve the equation.5.

Name: Answer the following questions 4.Find the explicit result for function
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Description: Answer the following questions 4.Find the explicit result for function y (i.e. function y = an function in term of x) of the initial valueproblem3xy=-y(0) = -4 .y+x*y'Verify that (e* sin y+3y)-(3x - e* sin y)y' = 0 is exact.Then solve the equation.5.

(4) Given differential equation is dydx=3xy+x2y y0=-4 It can be written as…

Answered: 4. Find the explicit result for…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Answer the following questions

4.
Find the explicit result for function y (i.e. function y = an function in term of x) of the initial value
problem
3x
y=-
y(0) = -4 .
y+x*y'
Verify that (e* sin y+3y)-(3x - e* sin y)y' = 0 is exact.
Then solve the equation.
5.

Expert Solution

Step 1

(4)

Given differential equation is

$\frac{d y}{d x} = \frac{3 x}{y + x^{2} y} y (0) = - 4$

It can be written as

$\frac{d y}{d x} = \frac{3 x}{y (1 + x^{2})}$

Now,

Using variable separable ,

$y d y = \frac{3 x}{1 + x^{2}} d x$

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