28.1.45 problem 46

Internal problem ID [4351]
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 : 46
Date solved : Monday, January 27, 2025 at 09:07:48 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 19

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

\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-x^{3} {\mathrm e}^{-3 c_{1}}\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 2.240 (sec). Leaf size: 33

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

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