15.5.8 problem 8

Internal problem ID [2944]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 8
Date solved : Monday, January 27, 2025 at 06:59:58 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 18

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

\[ y = -\frac {1}{\operatorname {LambertW}\left (-\frac {c_1}{x^{2}}\right ) x} \]

✓ Solution by Mathematica

Time used: 5.850 (sec). Leaf size: 35

DSolve[(y[x]+x*y[x]^2)+(x-x^2*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^2}\right )} \\ y(x)\to 0 \\ \end{align*}