Am am trying to solve an ODE for a linear spring system.
on one side of the equation we have the $Mx''+Bx'+kx$ that you would use for the homogeneous part.
Now I am trying to solve for the Particular Solution for a force of $3e^{6+t}$ I thought I could use Method of Undetermined Coefficients, but I am not sure what kind of guess to make. I have already tried $$x_p(t)=Ae^{6+t}$$
Here's an example table of what I am talking about from a textbook I used for reference
Example Guesses for g(x) My $g(t)= 3e^{6+t}$
Any Suggestions? Shall I resort to another method?
Thank you!
First, realize that $Ae^{6+t} = Ae^6e^t = Ce^t.$
Second, if $e^t$ is one of the homogeneous solutions, then you'll have to multiply it by $t$ and use $Cte^t$. Or even $Ct^2 e^t.$ It would help if posted the actual equation.