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?
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.