ODE
\[ y'''(x)-3 y'(x)+2 y(x)=e^x x^2 \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.162799 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {1}{972} e^x \left (27 x^4-36 x^3+36 x^2+12 (-2+81 c_3) x+8+972 c_2\right )+c_1 e^{-2 x}\right \}\right \}\]
Maple ✓
cpu = 0.029 (sec), leaf count = 36
\[\left [y \left (x \right ) = \left (\frac {1}{36} x^{2}-\frac {1}{27} x +\frac {1}{27}\right ) x^{2} {\mathrm e}^{x}+\textit {\_C1} \,{\mathrm e}^{x}+\textit {\_C2} \,{\mathrm e}^{-2 x}+\textit {\_C3} \,{\mathrm e}^{x} x\right ]\] Mathematica raw input
DSolve[2*y[x] - 3*y'[x] + y'''[x] == E^x*x^2,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^(2*x) + (E^x*(8 + 36*x^2 - 36*x^3 + 27*x^4 + 972*C[2] + 12*x*(-2 + 81*C[3])))/972}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x)+2*y(x) = x^2*exp(x), y(x))
Maple raw output
[y(x) = (1/36*x^2-1/27*x+1/27)*x^2*exp(x)+_C1*exp(x)+_C2*exp(-2*x)+_C3*exp(x)*x]