anonymous 5 years ago method of undetermined coefficients 4y''+8y'+13y=1, y(0)=0, y'(0)=1/13

1. anonymous

use the quadratic formula find the roots to the characteristic polynomial $4s ^{2}+8s+13=0$ then find all the solns to the corresponding homogenous D E . find a particular solution to the DE and put them together

2. anonymous

i got to the point $\left( -8\pm \sqrt{-144} \right)\div8$ bit confused with the negative square root

3. anonymous

do i have to get imaginary numbers involved?

4. anonymous

$\sqrt{-144}= 12i$

5. anonymous

$y _{p}=1/13$ is a particular soln to the DE

6. anonymous

the homo soln will be $y _{h}(t)= c _{1}e ^{t}\cos8/12t+c _{2}e ^{t} \sin8/12$

7. anonymous

add the part. soln to this, then use your init values to solve for $c _{1}, c _{2}$

8. anonymous

when u put 8/12 do you mean 12/8?

9. anonymous

yes sorry

10. anonymous

and can you put it in brackets please?

11. anonymous

actually, i get that now, dont worry bout brackets

12. anonymous

what do you mean

13. anonymous

ok

14. anonymous

thanks for all the help, i have the final answer as $y(x)=\exp(x)[(2/39)\sin ((3/2)x)]+(1/13)$ do you know if that is right?