Differential equation associated with primitive y = Ae3x + Be5x :

$\frac{d^2 y}{d x^2}-8 \frac{d y}{d x}+15 y=0$ $\frac{d^2 y}{d x^2}+8 \frac{d y}{d x}-15 y=0$ $\frac{d^2 y}{d x^2}+8 \frac{d y}{d x}+y=0$ none of these

$\frac{d^2 y}{d x^2}-8 \frac{d y}{d x}+15 y=0$

y = Ae3x + Be5x y' = 3 Ae3x + 5 Be5x y'' = 9 Ae3x + 25 Be5x therefore y'' − 8y + 15y = 0 Hence (1) is the correct answer.