## lilMissMindset 3 years ago this one is tricky. help please! y''-4y'+3y=2cosx+4sinx i'm having trouble getting the Yp!

1. him1618

You can try substituting y = asinx + bcosx

2. ChmE

why would that help. I'm in diff eq as well and I wasn't thinking about that.

3. him1618

its called th method of undetermined coefficients

4. him1618

put it on the left side....compare with coeffs on the right fr etermining a a and b

5. lilMissMindset

isn't it y=a cos x + b sinx + cx cos x + dx sin x

6. him1618

that is for a special case i think

7. lilMissMindset

what are the roots anyway? +i, -i aren't they like, twice? then it will be case 4?

8. ChmE

r^2 - 4r +3 = 0 (r - 3)(r-1) r= 3, 1

9. lilMissMindset

that is for the homo part

10. him1618

im telling you take y=asinx + bcosx substitute y'' and y' and y in the above eqn and compare LHS and RHS ull get 2 eqns in a and b determine a and b and you have your soln

11. lilMissMindset

i did that, i always get 0 for B. it's not supposed to be the answer.

12. him1618

im getting the answer as b=1, a=0 which means y=cos x y=cos x satisfies the above eqns

13. lilMissMindset

oh sorry. i looked at the wrong answer on my book. i am sorry. Our answer is right. Thank you!

14. him1618