29.25.8 problem 705

Internal problem ID [5295]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 705
Date solved : Monday, January 27, 2025 at 11:04:47 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (1-y x \right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (1+y x \right ) \left (1+x^{2} y^{2}\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.260 (sec). Leaf size: 42

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

\begin{align*} y \left (x \right ) &= -\frac {1}{x} \\ y \left (x \right ) &= \frac {{\mathrm e}^{\operatorname {RootOf}\left (-2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )-{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} {\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+1\right )}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 35

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

\begin{align*} y(x)\to -\frac {1}{x} \\ \text {Solve}\left [x y(x)-\frac {1}{x y(x)}-2 \log (y(x))&=c_1,y(x)\right ] \\ \end{align*}