Internal problem ID [8901]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1322.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }+2 x \left (3 x +2\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(x^2*(x+1)*diff(diff(y(x),x),x)+2*x*(3*x+2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\left (-4 \ln \relax (x )+4 \ln \left (x +1\right )-\frac {12 x^{3}+6 x^{2}-2 x +1}{3 \left (x +1\right ) x^{3}}\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 44
DSolve[2*x*(2 + 3*x)*y'[x] + x^2*(1 + x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (-\frac {1}{3 x^3}+\frac {1}{x^2}-\frac {3}{x}-\frac {1}{x+1}-4 \log (x)+4 \log (x+1)\right )+c_2 \\ \end{align*}