49.21.10 problem 4(b)

Internal problem ID [7740]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 4(b)
Date solved : Monday, January 27, 2025 at 03:11:13 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {y^{2}}{y x +x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 2.204 (sec). Leaf size: 21

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

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