ODE
\[ x y'''(x)-y''(x)-x y'(x)+y(x)=1-x^2 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0808538 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_1 x+i c_3 \sinh (x)-c_2 \cosh (x)+x^2+3\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={x}^{2}+3+{\it \_C1}\,x+{\it \_C2}\,{{\rm e}^{x}}+{\it \_C3}\,{{\rm e}^{-x}} \right \} \] Mathematica raw input
DSolve[y[x] - x*y'[x] - y''[x] + x*y'''[x] == 1 - x^2,y[x],x]
Mathematica raw output
{{y[x] -> 3 + x^2 + x*C[1] - C[2]*Cosh[x] + I*C[3]*Sinh[x]}}
Maple raw input
dsolve(x*diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = -x^2+1, y(x),'implicit')
Maple raw output
y(x) = x^2+3+_C1*x+_C2*exp(x)+_C3*exp(-x)