47.1.34 problem 34

Internal problem ID [7415]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 34
Date solved : Monday, January 27, 2025 at 02:53:36 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 5.193 (sec). Leaf size: 30

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

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