Internal problem ID [8782]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1202.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 15
dsolve(x^2*diff(diff(y(x),x),x)-2*x*(x+1)*diff(y(x),x)+2*(x+1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x c_{1}+c_{2} x \,{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 21
DSolve[2*(1 + x)*y[x] - 2*x*(1 + x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (\frac {1}{2} c_2 e^{2 x}+c_1\right ) \\ \end{align*}