Internal problem ID [8781]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1201.
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 }+x \left (2 x +1\right ) y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 34
dsolve(x^2*diff(diff(y(x),x),x)+x*(2*x+1)*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (2 x^{2}-4 x +3\right )}{x^{2}}+\frac {c_{2} {\mathrm e}^{-2 x} \left (2 x +3\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 42
DSolve[-4*y[x] + x*(1 + 2*x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-2 x} \left (c_1 (4 x+6)+c_2 e^{2 x} (2 (x-2) x+3)\right )}{4 x^2} \\ \end{align*}