Internal problem ID [6220]
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`]]
\[ \boxed {y^{\prime }-\frac {y-x y^{2}}{x +y x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 22
dsolve(diff(y(x),x)=(y(x)-x*y(x)^2)/(x+x^2*y(x)),y(x), singsol=all)
\[ y \left (x \right ) = x \,{\mathrm e}^{-\operatorname {LambertW}\left (x^{2} {\mathrm e}^{-2 c_{1}}\right )-2 c_{1}} \]
✓ Solution by Mathematica
Time used: 60.444 (sec). Leaf size: 31
DSolve[y'[x]==(y[x]-x*y[x]^2)/(x+x^2*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {W\left (e^{\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )} x^2\right )}{x} \]