Internal problem ID [5467]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page
28
Problem number: 5(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-y^{2} x +y}{y x^{2}+x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.071 (sec). Leaf size: 22
dsolve(diff(y(x),x)=(y(x)-x*y(x)^2)/(x+x^2*y(x)),y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{-\LambertW \left (x^{2} {\mathrm e}^{-2 c_{1}}\right )-2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 31
DSolve[y'[x]==(y[x]-x*y[x]^2)/(x+x^2*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\text {ProductLog}\left (e^{\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )} x^2\right )}{x} \\ \end{align*}