dydx y e3x in differential equationsSolutiondydx y e3x I

dy/dx - y = e^3x in differential equations

Solution

dy/dx - y = e^3x

It is a linear differential equation with integrating factor, I.F = e^{integral of (-1)dx} = e^-x

Thus, the solution is :- y*I.F = integral of [e^3x*I.F]dx

or, y*e^-x = integral of [e^3x*e^-x]dx = integral of (e^2x)dx

or, y*e^-x = (1/2)*e^2x + c

or, 2y = e^3x + 2c*e^x