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 = 0.0879552 (sec), leaf count = 36
\[\left \{\left \{y(x)\to c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x}+e^{x^2}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) ={{\rm e}^{\sqrt {2}x}}{\it \_C2}+{{\rm e}^{-\sqrt {2}x}}{\it \_C1}+{{\rm e}^{{x}^{2}}} \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(2^(1/2)*x)*_C2+exp(-2^(1/2)*x)*_C1+exp(x^2)