Question

Find the general solution: $\frac {dy}{dx}+3y=e^{-2x}$

Answer 1

The given differential equation is

Now, I.F = e$\int$pdx = e$\int$3dx = e3x

The solution of the given differential equation is given by the relation,

y(I.F.) = $\int$(Q×I.F)dx+C

⇒ye3x = $\int$(e-2x.e3x)+C

⇒ye3x = $\int$exdx+C

⇒ye3x = ex+C

⇒y = e-2x + Ce-3x

This is the required general solution of the given differential equation.