8.1.3.68 Higher order differential equations

Problem: Find the general solution of the corresponding homogeneous differential equation and the form of the particular solution for the higher order differential equation: \[ y^{(4)}-2 y^{\prime \prime \prime}+y^{\prime}-2 y=\left(x^{2}+x\right) e^{2 x}+1 \text {. } \] clip2net.com