Internal problem ID [8917]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1340.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\frac {2 \left (a x +2 b \right ) y^{\prime }}{x \left (a x +b \right )}+\frac {\left (2 a x +6 b \right ) y}{\left (a x +b \right ) x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(diff(y(x),x),x) = 2/x*(a*x+2*b)/(a*x+b)*diff(y(x),x)-(2*a*x+6*b)/(a*x+b)/x^2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{2}}{a x +b}+\frac {c_{2} x^{3}}{a x +b} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 23
DSolve[y''[x] == -(((6*b + 2*a*x)*y[x])/(x^2*(b + a*x))) + (2*(2*b + a*x)*y'[x])/(x*(b + a*x)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2 (c_2 x+c_1)}{a x+b} \\ \end{align*}