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

Question

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

do i have to get imaginary numbers involved?

anonymous · Answer

$$\sqrt{-144}= 12i$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yes sorry

anonymous · Answer

and can you put it in brackets please?

anonymous · Answer

actually, i get that now, dont worry bout brackets

anonymous · Answer

what do you mean

anonymous · Answer

ok

anonymous · Answer

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?