Question

Form the differential equation whose general solution is y = a cos 2x + b sin 2x.

Answer 1

y = a cos 2x + b sin 2x   ....(1)

∴ `dy/dx` = – 2a sin 2x + 2b cos 2x

Again differentiating w.r.t.x

∴ `(d^2y)/(dx^2)` = – 4a cos 2x – 4b sin 2x

= – 4(a cos 2x + b sin 2x)

= – 4y   ....[From (1)]

∴ `(d^2y)/(dx^2) + 4y` = 0