ODE No. 1051

\[ \left (4 x^2-3\right ) y(x)-e^{x^2}+y''(x)-4 x y'(x)=0 \]

✓ Mathematica : cpu = 0.0232011 (sec), leaf count = 44

DSolve[-E^x^2 + (-3 + 4*x^2)*y[x] - 4*x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to -e^{(x-1) x+x}+c_1 e^{(x-1) x}+\frac {1}{2} c_2 e^{(x-1) x+2 x}\right \}\right \}\]

✓ Maple : cpu = 0.049 (sec), leaf count = 27

dsolve(diff(diff(y(x),x),x)-4*x*diff(y(x),x)+(4*x^2-3)*y(x)-exp(x^2)=0,y(x))

\[y \left (x \right ) = {\mathrm e}^{x \left (1+x \right )} c_{2} +{\mathrm e}^{\left (x -1\right ) x} c_{1} -{\mathrm e}^{x^{2}}\]