Internal problem ID [9026]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1447.
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}+\frac {\left (-x -1\right ) y}{x^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 24
dsolve(diff(diff(y(x),x),x) = -1/x*diff(y(x),x)-(-x-1)/x^4*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {1}{x}}+c_{2} {\mathrm e}^{\frac {1}{x}} \expIntegral \left (1, \frac {2}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 24
DSolve[y''[x] == -(((-1 - x)*y[x])/x^4) - y'[x]/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {1}{x}} \left (c_1-c_2 \text {Ei}\left (-\frac {2}{x}\right )\right ) \\ \end{align*}