Question

The function y=8 sin⁡2x is a solution of the differential equation \(\frac{d^2 y}{dx^2}\)+4y=0.

(a) True

(b) False

I got this question in a job interview.

I'd like to ask this question from General and Particular Solutions of Differential Equation topic in division Differential Equations of Mathematics – Class 12

Answer 1

The correct choice is (a) True

Easy explanation: The given statement is true.

Consider the function y=8 sin⁡2x

Differentiating w.r.t x, we get

\(\frac{dy}{dx}\)=16 cos⁡2x –(1)

Differentiating (1) w.r.t x, we get

\(\frac{d^2 y}{dx^2}\)=-32 sin⁡2x

\(\frac{d^2 y}{dx^2}\)=-4(8 sin⁡2x )=-4y

⇒\(\frac{d^2 y}{dx^2}\)+4y=0.