$y=a e^{m x}+b e^{-m x}$ satisfies which of the following differential equations? |
$\frac{d y}{d x}-m y=0$ $\frac{d y}{d x}+m y=0$ $\frac{d^2 y}{d x^2}+m^2 y=0$ $\frac{d^2 y}{d x^2}-m^2 y=0$ |
$\frac{d^2 y}{d x^2}-m^2 y=0$ |
We have, $y=a e^{m x}+b e^{-m x}$ $\Rightarrow \frac{d y}{d x}=m a e^{m x}-m b e^{-m x}$ $\Rightarrow \frac{d^2 y}{d x^2}=m^2\left(a e^{m x}+b e^{-m x}\right)$ $\Rightarrow \frac{d^2 y}{d x^2}=m^2 y \Rightarrow \frac{d^2 y}{d x^2}-m^2 y=0$ Hence, option (d) is correct. |