# What is the general solution of the differential equation dy/dx=6e^x?

Oct 7, 2017

$y = 6 {e}^{x} - 4$

#### Explanation:

We have:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 6 {e}^{x}$

This is a FIrst Order Separable ODE so we can just separate the variables to get:

$\int \setminus \mathrm{dy} = \int \setminus 6 {e}^{x} \setminus \mathrm{dx}$

Both sides are directly integrable so if we integrate we get:

$y = 6 {e}^{x} + C$

Applying the initial Conditions, $y = 2$ when $x = 0$ we have:

$2 = 6 {e}^{0} + C \implies C = - 4$

$y = 6 {e}^{x} - 4$