28.1.51 problem 52

Internal problem ID [4357]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 52
Date solved : Monday, January 27, 2025 at 09:08:52 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} x^{2} y^{2}-2 y+\left (x^{3} y-x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 18

dsolve((x^2*y(x)^2-2*y(x))+( x^3*y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 6.591 (sec). Leaf size: 35

DSolve[(x^2*y[x]^2-2*y[x])+( x^3*y[x]-x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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