Internal problem ID [8945]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1366.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {2 x y^{\prime }}{x^{2}+1}+\frac {y}{\left (x^{2}+1\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 24
dsolve(diff(diff(y(x),x),x) = -2/(x^2+1)*x*diff(y(x),x)-1/(x^2+1)^2*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{\sqrt {x^{2}+1}}+\frac {c_{2}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 22
DSolve[y''[x] == -(y[x]/(1 + x^2)^2) - (2*x*y'[x])/(1 + x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x+c_1}{\sqrt {x^2+1}} \\ \end{align*}