77.1.19 problem 35 (page 40)

Internal problem ID [17909]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 35 (page 40)
Date solved : Tuesday, January 28, 2025 at 11:12:09 AM
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: 0.003 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.556 (sec). Leaf size: 56

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

\[ y(x)\to e^{-\frac {1}{4} x^2 \left (x^2+2\right )} \left (\int _1^x\frac {e^{\frac {1}{4} K[1]^2 \left (K[1]^2+2\right )}}{K[1]^3+K[1]}dK[1]+c_1\right ) \]