Find the general solution of the differential equations:`(dy)/(dx)+3y=e^(-2x)`

Explanation

`(dy)/(dx)+3y=e^(-2x)`
Here, `P=3`, `Q=e^(-2x)`
`I.F.=e^(intPdx)=e^(int3dx)=e^(3x)`
and general solution :
`y(I.F.)=intQ*(I.F.)dx+c`
`implies ye^(3x)=inte^(-2x)*e^(3x)d x +c`
`implies ye^(3x)=inte^(x)dx+c`
`implies ye^(3x)=e^(x)+c`
`implies y=e^(-2x)+c*e^(-3x)`