Internal problem ID [8900]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1321.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 15
dsolve(x^2*(x+1)*diff(diff(y(x),x),x)-x*(2*x+1)*diff(y(x),x)+(2*x+1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x c_{1}+c_{2} x \left (x +\ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 17
DSolve[(1 + 2*x)*y[x] - x*(1 + 2*x)*y'[x] + x^2*(1 + x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (c_2 (x+\log (x))+c_1) \\ \end{align*}