How Do I Solve y''+4y'+4y=2+3e^2x and Find Related Resources?

[franky2727]

unfortunatly i have lost a question paper which has questions like y''+y'+y=sinx or =e^2x or =X+2-4+e^2x or=2^-3x+5E^-5e etc etc, i have the questions and answers for the y''+y'+y=0 format questions but none of the non zero questions so my question is 2 fold

first of all how do i go about answering y''+4y'+4y=2+3e^2x

and second of all has anyone got leeds university MATH1400 sheet 4 questions for this year and if not which is the responce I'm expecting has anyone got any ideas where i can find examples of questions like this? thanks

 

[dynamicsolo]

You want to set up the "characteristic equation" for
y'' + 4y' + 4y = 0 first and solve this for the values of r which will give you the solutions y = e^(rx) for the homogeneous equation.

You will find that this has a repeated root. How do you handle that?

The next step will be to use something like the method of undetermined coefficients to find the "particular solution" for the non-homogenous equation you started with.