Question

If y = Asinx + Bcosx + xsinx, then

(A) d²y/dx² + y = cosx

(B) d²y/dx² + y = 2cosx

(C) d²y/dx² - y = 2sinx

(D) d²y/dx² - y = 2cosx

Answer 1

Answer is (B) d²y/dx² + y = 2cosx

y = Asinx + Bcosx + xsinx

Differentiating w.r.t. x, we get

y₁ = Acosx - Bsinx + sinx + xcosx

Again, differentiating w.r.t. x, we get

y₂ = -Asinx - Bcosx + cosx + cosx - xsinx

y₂ = -(Asinx + Bcosx + xsinx) + 2cosx

= - y + 2cosx