31.1.2 problem 1.2

Internal problem ID [5700]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 1.2
Date solved : Monday, January 27, 2025 at 01:08:15 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: 0.033 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 5.370 (sec). Leaf size: 30

DSolve[(y[x]^2+x*y[x]^2)+(x^2-y[x]*x^2)*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*}