81.3.5 problem 5

Internal problem ID [18623]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 12:04:31 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

dsolve(diff(y(x),x)+x/(1+x^2)*y(x)=1/(x*(1+x^2)),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\operatorname {arctanh}\left (\frac {1}{\sqrt {x^{2}+1}}\right )+c_{1}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 30

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

\[ y(x)\to \frac {-\text {arctanh}\left (\sqrt {x^2+1}\right )+c_1}{\sqrt {x^2+1}} \]