Find the general solution for a nonhomogenous equation.

cyturk
Messages
8
Reaction score
0

Homework Statement


Find the general solution for a nonhomogenous equation.
y''+4y=3csc2t

Homework Equations


The Attempt at a Solution


I simplified the equation to...
y''+4y=(3)/(sin(2t))

Then I guessed...
y=Asint+Bcost
y'=Acost-Bsint
y''=-Asint-BcostThen I got...
-Asint-Bcost+4Asint+4Bcost=(3)/(sin(2t))

Simplifies to...
3Asint+3Bcost=(3)/(2sintcost))

NOTE: Trig Identity: sin(2t)=2sintcost

I am stuck and I am not even sure if I took the correct steps.
 
Last edited:
Physics news on Phys.org
Variations of parameters.
 
hunt_mat said:
Variations of parameters.

Thanks for your help! I have been trying to figure out Variation of Parameters and I can't seem to find it on Khan Academy. Any chance there are any videos or resources you can suggest?
 
http://en.wikipedia.org/wiki/Variation_of_parameters" is always a good place as sometimes they'll give an example...like in what I posted.
 
Last edited by a moderator:
Thanks for everyone's help! I got a solution, although it kinda looks weird, but it makes sense to me now! :)
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
Replies
7
Views
2K
Diff. Eq. — Identifying Particular Solution Given solution family
Replies
4
Views
2K
2nd-order nonhomogeneous equation
Replies
7
Views
3K
Find the Cartesian equation given the parametric equations
Replies
6
Views
1K
2nd-order Nonhomogeneous Differential Equation
Replies
5
Views
2K
Find the general solution of the given PDE
Replies
3
Views
1K
How do we write a sinusoidal solution to a 2nd order DE as a sum of exponentials raised to complex roots?
Replies
2
Views
2K
What Makes the Undetermined Coefficients Method Fail with Sinusoidal Input?
Replies
12
Views
1K
Line Integral Problems on Ellipse Boundary | Compute Integrals Directly
Replies
1
Views
4K
How to get general solution via Green's function?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top