Question

What is the general solution for `dy/dx = 2y-3` ?

Answer 1

The solution is `y=(Ce^(2x)+3)/2`

Explanation:

The ODE is

`dy/dx=2y-3`

Therefore,

`dy/(2y-3)=dx`

`intdy/(2y-3)=intdx`

`1/2ln(2y-3)=x+C_1`

`ln(2y-3)=2(x+C_1)`

`2y-3=e^(2x+2C_1)=e^(2x)*e^(2C_1)=Ce^(2x)`

`y=(Ce^(2x)+3)/2`