ODE
\[ y''(x)+y(x)=e^x \left (x^2-1\right ) \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.282715 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {1}{2} e^x (x-2) x+c_1 \cos (x)+c_2 \sin (x)\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 21
\[\left [y \left (x \right ) = \sin \left (x \right ) \textit {\_C2} +\textit {\_C1} \cos \left (x \right )+\frac {x \left (x -2\right ) {\mathrm e}^{x}}{2}\right ]\] Mathematica raw input
DSolve[y[x] + y''[x] == E^x*(-1 + x^2),y[x],x]
Mathematica raw output
{{y[x] -> (E^x*(-2 + x)*x)/2 + C[1]*Cos[x] + C[2]*Sin[x]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x) = exp(x)*(x^2-1), y(x))
Maple raw output
[y(x) = sin(x)*_C2+_C1*cos(x)+1/2*x*(x-2)*exp(x)]