what is the solution to the nonhomogeneous equations: y''-9y=2xe^3x+5
y''+y=csc^2x

Question

what is the solution to the nonhomogeneous equations: y''-9y=2xe^3x+5
y''+y=csc^2x

amistre64 · Answer

this is more of a study site that guides you to get an answer rather than simply a site that will do your work for you.

amistre64 · Answer

is that a system of equations , or are you simply trying to get 2 questions answered by one post?

anonymous · Answer

Its two questions in one post and I just want help specifically with finding the particular solution

amistre64 · Answer

looks like they have constant coefficients; which means the homogenous part can be determined by a characteristic quadratic eqauation.

the particular parts tho, hmm.  the first appears to be workable from a table of "best guesses".

2xe^3x+5  best fits:  yp = (ax + b)e^3x + c

amistre64 · Answer

the second one tho would either have to take the long route or just go to a wonskian approach to shorten in up

amistre64 · Answer

$$\begin{vmatrix}W_1&W&W_2\ cos(x)&0&sin(x)\-sin(x)&csc^2(x)&cos(x)\end{vmatrix}$$