29.24.2 problem 664

Internal problem ID [5255]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 664
Date solved : Monday, January 27, 2025 at 10:49:54 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 25

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

\begin{align*} y \left (x \right ) &= -\frac {1}{x} \\ y \left (x \right ) &= -\frac {\operatorname {LambertW}\left (-x \,{\mathrm e}^{-c_{1}}\right )}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.002 (sec). Leaf size: 43

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

\begin{align*} y(x)\to -\frac {1}{x} \\ y(x)\to -\frac {W\left (-e^{-c_1} x\right )}{x} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{x} \\ \end{align*}