40.2.17 problem 42

Internal problem ID [6595]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 42
Date solved : Monday, January 27, 2025 at 02:14:57 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 18

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

\[ y = -\frac {1}{\operatorname {LambertW}\left (-\frac {c_1}{x^{3}}\right ) x} \]

✓ Solution by Mathematica

Time used: 6.431 (sec). Leaf size: 35

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

\begin{align*} y(x)\to -\frac {1}{x W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^3}\right )} \\ y(x)\to 0 \\ \end{align*}