83.5.15 problem 15

Internal problem ID [19110]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 12:57:14 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (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: 0.036 (sec). Leaf size: 33

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

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