# Find the differential equation whose solution is y=ae^(bx)?

Jun 18, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} - b y = 0$

#### Explanation:

As $y = a {e}^{b x}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = a \cdot {e}^{b x} \cdot b$

or $\frac{\mathrm{dy}}{\mathrm{dx}} = a \cdot \frac{y}{a} \cdot b = b y$

Hence differential equation is

$\frac{\mathrm{dy}}{\mathrm{dx}} - b y = 0$