ODE4.3

From Exampleproblems

$y''-y'+2y=10e^{-x}\sin(x)\,$

Find a particular solution $y_p\,$ , by finding a generalization of the equation which has the original problem as the complex part. $y_z\,$ is the imaginary particular part.

$(D^2-D+2)y_z = 10e^{(-1+i)x}\,$

The right hand side of the first equation is the complex part of the right hand side of the last equation. Solve for $y z$ and find the imaginary part of the answer. This will be the answer to the original problem.

$y_z = \frac{10e^{(-1+i)x}}{(-1+i)^2-(-1+i)+2}\,$