Solve the following differential equation : `(dy)/(dx)+2y=6e^x`

Explanation

`dy/dx=P(x)=Q(x)`

`IF=e^(intP(x)dx`

`IF=e^(2dx)=e^(2x)`

`y*(IF)=int(Q(x)IFdx`
`yxe^(2x)=int(6e^x)*e^(2x)dx`

`y*e^(2x)=6inte^(3x)dx`

`y*e^(2x)=6*e^(3x)/3+c`

`y=2e^(x)+e^(-2x)C`.