Internal problem ID [8833]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1253.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x \left (x +1\right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 16
dsolve(x*(x+1)*diff(diff(y(x),x),x)+(3*x+2)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \ln \left (x +1\right )+c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 28
DSolve[y[x] + (2 + 3*x)*y'[x] + x*(1 + x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \log (2 (x+1))+2 c_1}{\sqrt {2} x} \\ \end{align*}