# Given that y= ax+b is a solution of the differential equation dy/dx = 4x -2y, how do you find a and b?

Sep 27, 2016

$a = 2 , b = - 1$

#### Explanation:

If $y = a x + b$ is a solution of the differential equation $\frac{\mathrm{dy}}{\mathrm{dx}} = 4 x - 2 y$, then

$\frac{d}{\mathrm{dx}} \left(a x + b\right) = 4 x - 2 \left(a x + b\right)$ or

$a = 4 x - 2 a x - 2 b$ or

$\left\{\begin{matrix}a + 2 b = 0 \\ 4 - 2 a = 0\end{matrix}\right.$

Solving, for $a , b$

$a = 2 , b = - 1$