 Quandaries and Queries Who is asking: Student Level: All Question: I have a question that i really cant do, it is as follows: The ODE dy/dx + 0.5y = 0.5e-1.5x ; y(5) = 2 Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6 I think i should use an integrating factor but i cant do it. I hope someone can help. Hi David, First you need to solve the homogenous equation dy/dx + 0.5y = 0 You can solve this equation using the integration factor e-integral(0.5)dx = e-0.5x I actually looked at the equation as dy/dx = -0.5y and realized that y is a function which is almost identical to its own derivative so I substituted y = eax into the equation and found that a = -0.5 In either case you get the general solution of the homogenous equation to be y = k e-0.5x Now you need one solution of dy/dx + 0.5y = 0.5e-1.5x Since the right side is 0.5e-1.5x I guessed a solution of the form y = A e-1.5x Substitute this into dy/dx + 0.5y = 0.5e-1.5x and solve for A. When I did this I got A = - 0.5. Hence the general solution of dy/dx + 0.5y = 0.5e-1.5x is y = k e-0.5x - 0.5 e-1.5x Harley Go to Math Central