ODE No. 1320

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

✓ Mathematica : cpu = 0.106049 (sec), leaf count = 21

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

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

✓ Maple : cpu = 0.048 (sec), leaf count = 17

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

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