2.1211   ODE No. 1211

\[ 4 x^3 y'(x)+x^2 y''(x)+\left (4 x^4+2 x^2+1\right ) y(x)=0 \]

✓ Mathematica : cpu = 0.0293593 (sec), leaf count = 68

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

\[\left \{\left \{y(x)\to c_1 e^{-x^2} x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}}-\frac {i c_2 e^{-x^2} x^{\frac {1}{2}+\frac {i \sqrt {3}}{2}}}{\sqrt {3}}\right \}\right \}\]

✓ Maple : cpu = 0.078 (sec), leaf count = 36

dsolve(x^2*diff(diff(y(x),x),x)+4*x^3*diff(y(x),x)+(4*x^4+2*x^2+1)*y(x)=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{-x^{2}} \left (x^{\frac {1}{2}-\frac {i \sqrt {3}}{2}} c_{2} +x^{\frac {1}{2}+\frac {i \sqrt {3}}{2}} c_{1} \right )\]