Question

solve the equation (D^2 + 1)y=x sin x by the method of variation of parameters​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

We recall the concept of variation of parameters

Variation of parameters: It is a method to solve inhomogeneous linear ordinary differential equations.

Given:

$(D^{2}+1) y=xsinx$

Auxillary equation is

$m^{2}+1=0$

$m=+-i$

$Y_{p}=Acosx+Bsinx$

$y_{1} =cosx\\y_{2} =sinx$

By variation of parameters,

$Y_{p}(x)=-cosx integralof xsin^{2}x+sinxIntegral of xsinxcosx$