Try using variation of parameters: Method of variation of parametersHello to everybody!
I'm trying to solve the following ODE:
y"(t) -5·y'(t) +6·y(t) = 2·tan (2·t)
here's what I have till now:
(D^2-5D+6)y = 0 is the homogeneous part
y_h = A*e^(2t) + B*e^(3t)
What can I do for the particular solution?
In general I know 2 methods - the ansatz with the characteristic polynomial when the inhomogeneous part is a function of the form: a*e^(bx) (a, b are complex numbers) and the Laplace-transform.
Unfortunatelly neither helps me finding y_p and I know it does exist, cuz Mathematica has given it
I really hope you could help me If the solution is too difficult to be done manually, then I would be glad to see it described with words or some general formulae.
best wishes and 10x