35.4.10 problem 10

Internal problem ID [6128]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 10
Date solved : Monday, January 27, 2025 at 01:37:44 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 14

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

\[ y = \frac {x}{\operatorname {LambertW}\left (c_1 \,x^{2}\right )} \]

✓ Solution by Mathematica

Time used: 4.162 (sec). Leaf size: 27

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

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