2.1351   ODE No. 1351

\[ y''(x)=\frac {y(x)}{x^4}-\frac {\left (2 x^2+1\right ) y'(x)}{x^3} \]

✓ Mathematica : cpu = 0.0110924 (sec), leaf count = 50

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

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

✓ Maple : cpu = 0.052 (sec), leaf count = 24

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

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