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Chapter 8: Q5P (page 403)

Using (3.9), find the general solution of each of the following differential equations. Compare a computer solution and, if necessary, reconcile it with yours. Hint: See comments just after (3.9), and Example 1.

y'cosx+y=cos2x

Short Answer

Expert verified

Answer:

The general solution of the differential equation is y=x-cosx+Csexx+tanx.

Step by step solution

01

Given information

The given differential equation isy'cosx+y=cos2x.

02

Meaning of the first-order differential equation

A first-order differential equation is defined by two variables, x and y, and its function f(x,y)is defined on an XY-plane region.

03

Find the general solution

Write this differential equation to make it in the form y'+Py=Q; that is

y'+ysecx=cosx

From equation 3.4,

I=鈭�secxdx=Insecx+tanxeI=eInsecx+tanx=secx+tanx.

Find a solution for this differential equation.

Therefore, the general solution of the differential equation is.

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