Question

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

Answer 1

`a = 2, b = -1`

Explanation:

If `y= ax+b` is a solution of the differential equation `dy/dx = 4x -2y`, then

`d/(dx)(ax+b) = 4x-2(ax+b)` or

`a = 4x-2ax-2b` or

`{(a+2b=0),(4-2a=0):}`

Solving, for `a,b`

`a = 2, b = -1`