Undetermined coefficients Definition and 110 Threads

I am looking for the form of a solution for a second order ODE with right hand side: x (sin x + 2) I'm thinking the form would be (Ax + B) sin(x) + (Cx + D) cos(x) + Ex + F. Does this seem correct? Thanks for any help or suggestions!

Hi, I'm having a bit of trouble with a problem here. The question is: Use the Method of undetermined coefficients to Find the general solution to th system: dx/dt = y + e^t dy/dt = -2x + 3y + 1 I've got the homogenous solution fine, however I'm having a bit of difficulty with the...

Homework Statement Find the solution for y"+2y'+5y=(e^x)sinx Homework Equations The Attempt at a Solution So far I think I've gotten the solution from the characteristic equation, but I'm having trouble with the particular solution. For the characteristic equation solution...

Homework Statement Solve the following initial value problem y'' - 5y' +6y = x*exp(2x), y(0) = y'(0) = 0 Homework Equations The Attempt at a Solution Ive found the complimentary solution to be r = 3, 2, Yg = C1*exp(3x) + C2*exp(2x) + Yp But to find Yp is giving me the...

y" + 0.5y' + y = 1-cos(t); y(0) = y'(0) = 0 I used method of undetermined coefficients to get particular solution: Y(t) = -2sin(t) + 1 To get homogeneous solution, I solved characteristic equation to get complex roots: r_1,2 = -1/4 +- i*sqrt(15)/4 so homogeneous solution is: y...

hello everyone, i need some huge help here. here's the equation : y''+y'-6y=10e^2x-18e^3x-6x-11. complementary solution:c1e^2x+c2e^-3x s1={e^2x} s2={e^3x} s3=(x,1} ok since e^2x exists in the complimentary solution, it is therefore a solution, so i multiply it by x to get s'1{xe^2x}...

I know how to solve the following ODE with variation of parameters: y''+4y=4\sec{\left(2t\right)}. Is there any way to solve this with undetermined coefficients? So far I have tried Yp=Acos(2t)+Bsin(2t), but that didn't work. Thanks for the help.

Sup' all? Ok, I have a quick question (hopefully). I'm trying to use the method of undetermined coefficients, and I keep getting stuck at one specific spot in the method. I'm not exactly sure what I'm doing. Let me try and explain: The problem is given as: 2y''+3y'+y=t^2+3*\sin t Which...

Hello, I have this DE: y'' + 2y' - 3y = 8ex - 12e3x when I find homogeneous solution I get yh = c1ex + c2e-3x; so now to find the particular solution by method of undetermined coefficients, do I set y to smth like this: y = y1 + y2 where y1 = Axex, y2 = A3x ? since one...

(d^2x/dt^2)+(w^2)x=Fsin(wt), x(0)=0,x'(0)=0 Hope that's readable. First part is second derivative of x with respect to t. w is a constant and F is a constant. I need to find a solution to this using method of undetermined coeffecients and I'm confused with all the different variables. Anyone...