28.1.113 problem 136

Internal problem ID [4419]
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 : 136
Date solved : Monday, January 27, 2025 at 09:16:29 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 32

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

\[ y \left (x \right ) = \frac {\sqrt {6}\, {\mathrm e}^{\frac {c_{1}}{2}}}{2 \sqrt {-\frac {{\mathrm e}^{c_{1}}}{x \operatorname {LambertW}\left (-\frac {2 \,{\mathrm e}^{c_{1}}}{3 x}\right )}}} \]

✓ Solution by Mathematica

Time used: 7.419 (sec). Leaf size: 78

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

\begin{align*} y(x)\to -i \sqrt {\frac {3}{2}} \sqrt {x} \sqrt {W\left (-\frac {2 e^{c_1}}{3 x}\right )} \\ y(x)\to i \sqrt {\frac {3}{2}} \sqrt {x} \sqrt {W\left (-\frac {2 e^{c_1}}{3 x}\right )} \\ y(x)\to 0 \\ \end{align*}