Practicing Success
Practicing Success
CUET Preparation Today
Which one of the following is a differential equation of the family of curves $y=A e^{2 x}+B e^{-2 x}$ |
$\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+2 y=0$ $x \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}-x y+x^2-2=0$ $\frac{d^2 y}{d x^2}=4 y$ $\left(\frac{d y}{d x}\right)^3=4 y\left(x \frac{d y}{d x}-2 y\right)$ |
$\frac{d^2 y}{d x^2}=4 y$ |
$y=A^{2 x}+b e^{-2 x} \Rightarrow \frac{d y}{d x}=2\left(A^{2 x}-b e^{-2 x}\right) $ $\frac{d^2 y}{d x^2}=4\left(Ae^{2 x}+b e^{-2 x}\right)=\ln y$ Hence (3) is the correct answer. |
