solved by Luca Imponenti
Complete the solution to the following problem
![{\displaystyle y''+4y'+13y=2e^{-2x}cos(3x)\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa8856fe667dfd446436d60b60e40b2c4fd97c63)
where
and
Find the overall solution
corresponds to the initial condition:
![{\displaystyle y(0)=1\ ,\ y'(0)=0\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/583283c322ca54967e07641dbc6f6d3715cebe73)
- Plot the solution over 3 periods.
Taking the derivatives of the particular solution
Plugging these into the ODE yields
Equating like terms allows us to solve for M and N
So the particular solution is
The overall solution in the sum of the homogeneous and particular solutions
To find A and B we apply the initial conditions
Taking the derivative
Giving us the overall solution
The period for
is
Plotting the solution
over 3 periods yields
Egm4313.s12.team11.imponenti (talk) 01:56, 30 March 2012 (UTC)