Internal problem ID [8911]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1332.
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 {\left (3 x +1\right ) y}{4 x^{2} \left (x +1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 19
dsolve(diff(diff(y(x),x),x) = 1/(x+1)*diff(y(x),x)-1/4*(3*x+1)/x^2/(x+1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}+c_{2} \sqrt {x}\, \left (x +\ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 21
DSolve[y''[x] == -1/4*((1 + 3*x)*y[x])/(x^2*(1 + x)) + y'[x]/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} (c_2 (x+\log (x))+c_1) \\ \end{align*}