Question

For the differential equation, find the general solution:

`dy/dx + 3y = e^(-2x)`

Answer 1

`dy/dx + 3y = e^(- 2x)`    ...(i)

This is a linear differential equation of the form `dy/dx Py = Q` Here

P = 3 and Q = e^-2x 

∴ I.F. = `e^(int P dx) = e^(int 3 dx) = e^(3x)`

The general solution of the fundamental equation,

y(I.F.) = ∫ Q × I.F. dx + C

ye^3x = ∫ e^-2x · e^3x + C

ye^3x = ∫ e^x + C

ye^3x = e^x + C

y = e^-2x + Ce^-3x