Internal problem ID [3860]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 6.1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {x y}{x^{2}+1}-\frac {1}{2 x \left (x^{2}+1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 24
dsolve(diff(y(x),x)+x/(1+x^2)*y(x)=1/(2*x*(1+x^2)),y(x), singsol=all)
\[ y \relax (x ) = \frac {-\frac {\arctanh \left (\frac {1}{\sqrt {x^{2}+1}}\right )}{2}+c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 33
DSolve[y'[x]+x/(1+x^2)*y[x]==1/(2*x*(1+x^2)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\tanh ^{-1}\left (\sqrt {x^2+1}\right )-2 c_1}{2 \sqrt {x^2+1}} \\ \end{align*}