ODE
\[ \left (x^2+2\right ) y'''(x)+\left (x^2+2\right ) y'(x)-2 x y''(x)-2 x y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.114606 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {1}{4} \left (2 c_1 x^2+2 i c_2 e^{-i x}-c_3 e^{i x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.103 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}+{\it \_C2}\,\cos \left ( x \right ) +{\it \_C3}\,\sin \left ( x \right ) \right \} \] Mathematica raw input
DSolve[-2*x*y[x] + (2 + x^2)*y'[x] - 2*x*y''[x] + (2 + x^2)*y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*x^2*C[1] + ((2*I)*C[2])/E^(I*x) - E^(I*x)*C[3])/4}}
Maple raw input
dsolve((x^2+2)*diff(diff(diff(y(x),x),x),x)-2*x*diff(diff(y(x),x),x)+(x^2+2)*diff(y(x),x)-2*x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*x^2+_C2*cos(x)+_C3*sin(x)