I have to solve the given Dif. EQs with the initial conditions that are given.
But, the hard part is I'm not allowed to use the same method twice. (That is, I can only use separation of variables once, variation of parameters once, etc).
1.)
2.)
3.)
4.)
I solved #2 using method of undetermined coefficients, so I don't need help on that anymore. Now I have #1 and #4 left (and if someone could check my #3). For #1, I think I have to use an integrating factor.....but not sure how to separate it into standard form first.. ...
That leaves me with #4... how can I solve this without using undetermined coefficients, separation of variables and integrating factor.. there's a method that is something involving constant coefficients, but not sure how to use that. I think I find y_c first and then y_p after... I can easily find y_c..its trying to find y_p that's hard.
Thanks a lot Kriz. I need some help finishing the integrating factor one:
And so our integrating factor is:
Multiply by both sides of the equation.
Now this is where things get fuzzy. Is it just:
And then take integrals of both sides (which the integral of the derivative on the left will just leave what that is, so I just have to integrate the right side)...or is this step wrong?