77.1.22 problem 38 (page 41)

Internal problem ID [17912]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 38 (page 41)
Date solved : Tuesday, January 28, 2025 at 11:12:16 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 47

dsolve(diff(y(x),x)-x*y(x)/(2*(x^2-1))-x/(2*y(x))=0,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {\sqrt {x -1}\, \sqrt {x +1}\, c_{1} +x^{2}-1} \\ y &= -\sqrt {\sqrt {x -1}\, \sqrt {x +1}\, c_{1} +x^{2}-1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.628 (sec). Leaf size: 53

DSolve[D[y[x],x]-x*y[x]/(2*(x^2-1))-x/(2*y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x^2+c_1 \sqrt {x^2-1}-1} \\ y(x)\to \sqrt {x^2+c_1 \sqrt {x^2-1}-1} \\ \end{align*}