y''=2y+2tan^3x yp(x)=tanx
r^2=0
What the eff do I do here?

Question

y''=2y+2tan^3x  yp(x)=tanx
r^2=0 
What the eff do I do here?

anonymous · Answer

this one and then im really going to sleep lol

anonymous · Answer

or do I just take the y'' of tanx then solve for y from the right side

abb0t · Answer

how about you rewrite it to: $y"-2y=2tan^3(x)$

abb0t · Answer

since you're dealing with tangent, I would use variation of parameters, since there are no restrictions.

abb0t · Answer

$r^2-2$ and you have: $r= \pm \sqrt{2}$

anonymous · Answer

yeah that's a good call but the variation of parameters is chapter 4.6 and this homework is 4.5 so do you think it could be solved

anonymous · Answer

without cramers rule

abb0t · Answer

You could, you'd have to change tangent to sines and cosines though, because you can't use undetermined coefficients with tangent, only exponential, polynomial, sine or cosine, or combinations of those.

anonymous · Answer

yeah I think it could cause we aren't deriving it quite yet they already give us the particular solution

abb0t · Answer

in that case, all you need is your complementary solution, remember the general solution is $Y = Y_c+Y_p$

anonymous · Answer

yes sir that is it. thanks for the help!