ODE
\[ -y'''(x)+y''''(x)-3 y''(x)+5 y'(x)-2 y(x)=e^{3 x} \] ODE Classification
[[_high_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.192997 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {e^{3 x}}{40}+c_1 e^{-2 x}+e^x (x (c_4 x+c_3)+c_2)\right \}\right \}\]
Maple ✓
cpu = 0.027 (sec), leaf count = 33
\[\left [y \left (x \right ) = \frac {{\mathrm e}^{3 x}}{40}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-2 x}+\textit {\_C3} x \,{\mathrm e}^{x}+\textit {\_C4} \,{\mathrm e}^{x} x^{2}\right ]\] Mathematica raw input
DSolve[-2*y[x] + 5*y'[x] - 3*y''[x] - y'''[x] + y''''[x] == E^(3*x),y[x],x]
Mathematica raw output
{{y[x] -> E^(3*x)/40 + C[1]/E^(2*x) + E^x*(C[2] + x*(C[3] + x*C[4]))}}
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+5*diff(y(x),x)-2*y(x) = exp(3*x), y(x))
Maple raw output
[y(x) = 1/40*exp(3*x)+_C1*exp(x)+_C2*exp(-2*x)+_C3*x*exp(x)+_C4*exp(x)*x^2]