Internal problem ID [8976]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1397.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x^{4}}-\frac {y}{x^{5}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(diff(y(x),x),x) = -1/x^4*diff(y(x),x)+1/x^5*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} x \left (-\Gamma \left (\frac {2}{3}\right ) \Gamma \left (\frac {1}{3}, -\frac {1}{3 x^{3}}\right ) \sqrt {3}+2 \pi \right ) \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 27
DSolve[y''[x] == y[x]/x^5 - y'[x]/x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} c_2 E_{\frac {2}{3}}\left (-\frac {1}{3 x^3}\right )+c_1 x \\ \end{align*}