Internal problem ID [8905]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1326.
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 +1}+\frac {y}{x \left (x +1\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(diff(y(x),x),x) = -1/(x+1)*diff(y(x),x)-1/x/(x+1)^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{x +1}+\frac {c_{2} \left (x \ln \relax (x )-1\right )}{x +1} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 26
DSolve[y''[x] == -(y[x]/(x*(1 + x)^2)) - y'[x]/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 x+c_2 x \log (x)-c_2}{x+1} \\ \end{align*}