1. ## ODE resonance clarification

I tried using an online calculator for y''-3y'+2y=2x+4e3x and the answer they gave was y=c1e2x+c2ex+x+1.5+2e3x .However, isn't the yp part wrong as the answer neglected the fact that there is resonance?

2. ## Re: ODE resonance clarification

There is no resonance. The roots of the characteristic polynomial are 1 and 2, not 3.

3. ## Re: ODE resonance clarification

I see, but could 2 in 2x not be considered as a root?

4. ## Re: ODE resonance clarification

No. The right hand side has nothing to do with the characteristic polynomial.

The roots 1 and 2 give terms in $e^{x}$ and $e^{2x}$ to form the complementary solution. These could only resonate with forcing terms (the right hand side) in $e^{x}$ and $e^{2x}$ respectively.