Internal problem ID [8931]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1352.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {2 \left (x +a \right ) y^{\prime }}{x^{2}}+\frac {y b}{x^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
dsolve(diff(diff(y(x),x),x) = -2/x^2*(x+a)*diff(y(x),x)-b/x^4*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {-\sqrt {a^{2}-b}+a}{x}}+c_{2} {\mathrm e}^{\frac {\sqrt {a^{2}-b}+a}{x}} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 51
DSolve[y''[x] == -((b*y[x])/x^4) - (2*(a + x)*y'[x])/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {a-\sqrt {a^2-b}}{x}} \left (c_1 e^{\frac {2 \sqrt {a^2-b}}{x}}+c_2\right ) \\ \end{align*}