Question

solve the differential equation (D^2+1)y=sin^2(x)​

Answer 1

Answer:

Step-by-step explanation:

differentiate Y(p) twice to get Yp''.

Now substitute Yp'' and Yp in

Yp''+4Yp = ½-½cos2x

And equate like-coefficients.

You should get k0=1/8; N=-1/8 and M=0

So, your particular integral Yp is

Yp=⅛-⅛xsin2x

And hence, your complete solution is y=Yc+Yp, i.e

Complete solution ::

y = Acos2x+Bsin2x+⅛-⅛xsin2x

Answer 2

https://www.youtube.com/watch?v=FpVdRIrTJ0g