CUET Preparation Today
If $y=36 e^{5 x}+47 e^{-5 x}$, then |
$\frac{d^2 y}{d x^2}=-25 y$ $\frac{d^2 y}{d x^2}=5 y$ $\frac{d^2 y}{d x^2}=-5 y$ $\frac{d^2 y}{d x^2}=25 y$ |
$\frac{d^2 y}{d x^2}=25 y$ |
The correct answer is Option () - $y=36e^{5x}+47e^{-5x}.$ $\frac{dy}{dx}=36\cdot5e^{5x}-47\cdot5e^{-5x}=180e^{5x}-235e^{-5x}.$ $\frac{d^2y}{dx^2}=180\cdot5e^{5x}+235\cdot5e^{-5x}=900e^{5x}+1175e^{-5x}.$ $\frac{d^2y}{dx^2}=25(36e^{5x}+47e^{-5x}).$ $\frac{d^2y}{dx^2}=25y.$ |
