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Chapter 8: Q8-3-11P (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'+ycosx=sin2x

Short Answer

Expert verified

The general solution of the differential equations is y=2(sinx-1)+Ce-sinx

Step by step solution

01

Given Information.

The given differential equations isy'+ycosx=sin2x

02

Step 2: 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 formy'+Py=Q, from eq. 3.4

I=鈭�cosxdx=sinxeI=esinx

Find a solution for this differential equation

yeI=鈭�(sin2x)esinxdx=2esinx(sinx-1)+Cy=2(sinx-1)+Ce-sinx

Therefore, the general solution of the differential equations isy=2(sinx-1)+Ce-sinx .

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