Question

Y'=36y+72

find general solution to the equation.

Answer 1

`y'=36y+72`

`y'-36y=72`

`e^(-36t)y'-36e^(-36t)y=72e^(-36t)`

`(\mathrm d)/(\mathrm dt)[e^(-36t)y]=72e^(-36t)`

`e^(-36t)y=72\displaystyle\int e^(-36t)\,\mathrm dt`

`e^(-36t)y=-2e^(-36t)+C`

`y=-2+Ce^(36t)`