Question

Let $y=A~cos(x)+B~sin(x)$ the differential equation by eliminating A and B constants is given by:

• A. $\frac{d^{2}y}{dx^{2}}-y^{2}=0$
• B. $\frac{d^{2}y}{dx^{2}}+y^{2}=0$
• C. $\frac{d^{2}y}{dx^{2}}-y=0$
• D. $\frac{d^{2}y}{dx^{2}}+y=0$

Hint:

For solutions involving $sin(ax)$ and $cos(ax)$, the resulting differential equation is always $y'' + a^2y = 0$. Here $a=1$.

Answer 1

The Correct Option is D