(a) y = a cosx +b sin x is the solution of the differential equation (i) d^2y/dx^2 + y = 0 (ii) d^2y /dx^2 -y = 0 (iii) dy/dx + y = 0

Question

(a) y = a cosx +b sin x is the solution of the differential equation

(i) \(\frac{d^2y}{dx^2} + y = 0\)

(ii) \(\frac{d^2y}{dx^2} - y = 0\)

(iii) \(\frac{dy}{dx} + y = 0\)

(iv) \(\frac{dy}{dx} + x\frac{dy}{dx} = 0\)

(b) Find the solution of the differential equation

\( x\frac{dy}{dx} + 2y = x^2 , (x≠0)\) given that y = 0 When x = 1

Answer 1

(a) (i) \(\frac{d^2y}{dx^2} + y = 0\)

(b) Given; x\(\frac{dy}{dx} + 2y = x^2, (x​≠0)\)