ODE
\[ y''(x)-2 y(x)=4 e^{x^2} x^2 \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.23869 (sec), leaf count = 36
\[\left \{\left \{y(x)\to e^{x^2}+c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 26
\[\left [y \left (x \right ) = {\mathrm e}^{\sqrt {2}\, x} \textit {\_C2} +{\mathrm e}^{-\sqrt {2}\, x} \textit {\_C1} +{\mathrm e}^{x^{2}}\right ]\] Mathematica raw input
DSolve[-2*y[x] + y''[x] == 4*E^x^2*x^2,y[x],x]
Mathematica raw output
{{y[x] -> E^x^2 + E^(Sqrt[2]*x)*C[1] + C[2]/E^(Sqrt[2]*x)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-2*y(x) = 4*x^2*exp(x^2), y(x))
Maple raw output
[y(x) = exp(2^(1/2)*x)*_C2+exp(-2^(1/2)*x)*_C1+exp(x^2)]