Which one of the following is a differential equation of the family of curves $y=A e^{2 x}+B e^{-2 x}$
Answer & explanation
Correct answer: option 3
$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.