ODE
\[ -8 x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=4 e^{-x^2} x^3 \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.179666 (sec), leaf count = 38
\[\left \{\left \{y(x)\to \frac {1}{9} e^{-x^2} \left (-3 x^2+9 c_1 e^{3 x^2}-1+9 c_2\right )\right \}\right \}\]
Maple ✓
cpu = 0.056 (sec), leaf count = 32
\[\left [y \left (x \right ) = {\mathrm e}^{2 x^{2}} \textit {\_C2} +{\mathrm e}^{-x^{2}} \textit {\_C1} -\frac {x^{2} {\mathrm e}^{-x^{2}}}{3}\right ]\] Mathematica raw input
DSolve[-8*x^3*y[x] - (1 + 2*x^2)*y'[x] + x*y''[x] == (4*x^3)/E^x^2,y[x],x]
Mathematica raw output
{{y[x] -> (-1 - 3*x^2 + 9*E^(3*x^2)*C[1] + 9*C[2])/(9*E^x^2)}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(2*x^2+1)*diff(y(x),x)-8*x^3*y(x) = 4*x^3*exp(-x^2), y(x))
Maple raw output
[y(x) = exp(2*x^2)*_C2+exp(-x^2)*_C1-1/3*x^2*exp(-x^2)]