Find the particular solution of the differential equation dy

Solution

solution: if you have dy/dx + P(x)*y = Q(x) then the integrating factor is e^?P(x) dx = V Multiply V to both sides... then the left side becomes the derivative of V*y... here the integrating factor is e^(2x) thus e^(2x)dy/dx + 2e^(2x)y = 5e^(2x) then D[e^(2x)*y] = 5e^(2x) integrating... e^(2x)*y = 5/2 e^(2x) + C y = 5/2 + Ce^(-2x) ... given also that y(0) = 0 0 = 5/2 + C thus y = 5/2 - 5/2e^(-2x) ans