ODE
\[ y'''(x)-3 y''(x)+3 y'(x)-y(x)=x \left (1-e^x x^2\right ) \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0607558 (sec), leaf count = 42
\[\left \{\left \{y(x)\to c_3 e^x x^2+x \left (c_2 e^x-1\right )+c_1 e^x-\frac {1}{120} e^x x^6-3\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac { \left ( -{x}^{6}+120\,{\it \_C3}\,{x}^{2}+120\,{\it \_C2}\,x+120\,{\it \_C1} \right ) {{\rm e}^{x}}}{120}}-x-3 \right \} \] Mathematica raw input
DSolve[-y[x] + 3*y'[x] - 3*y''[x] + y'''[x] == x*(1 - E^x*x^2),y[x],x]
Mathematica raw output
{{y[x] -> -3 - (E^x*x^6)/120 + E^x*C[1] + x*(-1 + E^x*C[2]) + E^x*x^2*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+3*diff(y(x),x)-y(x) = x*(1-x^2*exp(x)), y(x),'implicit')
Maple raw output
y(x) = 1/120*(-x^6+120*_C3*x^2+120*_C2*x+120*_C1)*exp(x)-x-3