ODE
\[ -\left (3-4 x^2\right ) y(x)+y''(x)-4 x y'(x)=e^{x^2} \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0295146 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {1}{2} e^{(x-1) x} \left (c_2 e^{2 x}+2 c_1-2 e^x\right )\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 27
\[ \left \{ y \left ( x \right ) ={{\rm e}^{ \left ( 1+x \right ) x}}{\it \_C2}+{{\rm e}^{x \left ( -1+x \right ) }}{\it \_C1}-{{\rm e}^{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[-((3 - 4*x^2)*y[x]) - 4*x*y'[x] + y''[x] == E^x^2,y[x],x]
Mathematica raw output
{{y[x] -> (E^((-1 + x)*x)*(-2*E^x + 2*C[1] + E^(2*x)*C[2]))/2}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-4*x*diff(y(x),x)-(-4*x^2+3)*y(x) = exp(x^2), y(x),'implicit')
Maple raw output
y(x) = exp((1+x)*x)*_C2+exp(x*(-1+x))*_C1-exp(x^2)