Question

How do you find all solutions of the differential equation `dy/dx=2y-5`?

Answer 1

`y= C e^(2x) +5/2`

Explanation:

In this case , the variables are seperable `1/(2y-5) dy =dx`

Or`1/2 dy/(y-5/2) =dx` Now, integrate both sides, to get

`1/2 ln(y-5/2) = x+C1`

`ln (y-5/2)= 2x +2C1`

`y=5/2 +e^(2x +2C1)`

`y= C e^(2x) +5/2`