Internal problem ID [4368]
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]
\[ \boxed {y^{\prime }+\frac {x y}{x^{2}+1}=\frac {1}{2 x \left (x^{2}+1\right )}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x)+x/(1+x^2)*y(x)=1/(2*x*(1+x^2)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\operatorname {arctanh}\left (\frac {1}{\sqrt {x^{2}+1}}\right )+2 c_{1}}{2 \sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 33
DSolve[y'[x]+x/(1+x^2)*y[x]==1/(2*x*(1+x^2)),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\text {arctanh}\left (\sqrt {x^2+1}\right )-2 c_1}{2 \sqrt {x^2+1}} \]