2.1397   ODE No. 1397

\[ y''(x)=\frac {y(x)}{x^5}-\frac {y'(x)}{x^4} \]

✓ Mathematica : cpu = 0.0637579 (sec), leaf count = 38

DSolve[Derivative[2][y][x] == y[x]/x^5 - Derivative[1][y][x]/x^4,y[x],x]
 

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

✓ Maple : cpu = 0.144 (sec), leaf count = 27

dsolve(diff(diff(y(x),x),x) = -1/x^4*diff(y(x),x)+1/x^5*y(x),y(x))
 

\[y \left (x \right ) = x \left (2 \sqrt {3}\, \pi c_{2} -3 \Gamma \left (\frac {2}{3}\right ) \Gamma \left (\frac {1}{3}, -\frac {1}{3 x^{3}}\right ) c_{2} +c_{1} \right )\]