60.3.360 problem 1366

Internal problem ID [11370]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1366
Date solved : Monday, January 27, 2025 at 11:18:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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)
 

\[ y = \frac {c_{1} x +c_{2}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 2.139 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}] == -(y[x]/(1 + x^2)^2) - (2*x*D[y[x],x])/(1 + x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x+c_1}{\sqrt {x^2+1}} \]