Internal problem ID [5318]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }-\frac {y^{2}}{x y+x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve(diff(y(x),x)=y(x)^2/(x*y(x)+x^2),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (\frac {{\mathrm e}^{-c_{1}}}{x}\right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 2.271 (sec). Leaf size: 21
DSolve[y'[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*}