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 = 0.0205005 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {1}{972} e^x \left (12 \left (81 c_3-2\right ) x+972 c_2+27 x^4-36 x^3+36 x^2+8\right )+c_1 e^{-2 x}\right \}\right \}\]
Maple ✓
cpu = 0.042 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={\it \_C2}\,{{\rm e}^{-2\,x}}+{\frac {{{\rm e}^{x}}}{36} \left ( {x}^{4}-{\frac {4\,{x}^{3}}{3}}+{\frac {4\,{x}^{2}}{3}}+36\,x{\it \_C3}+36\,{\it \_C1} \right ) } \right \} \] 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),'implicit')
Maple raw output
y(x) = _C2*exp(-2*x)+1/36*exp(x)*(x^4-4/3*x^3+4/3*x^2+36*x*_C3+36*_C1)