Internal problem ID [1015]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }-\frac {x^{2}+y x +y^{2}}{y x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x)=(x*y(x)+x^2+y(x)^2)/(x*y(x)),y(x), singsol=all)
\[ y \left (x \right ) = x \left (-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-1-c_{1}}}{x}\right )-1\right ) \]
✓ Solution by Mathematica
Time used: 4.422 (sec). Leaf size: 31
DSolve[y'[x]==(x*y[x]+x^2+y[x]^2)/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \left (1+W\left (-\frac {e^{-1-c_1}}{x}\right )\right ) \\ y(x)\to -x \\ \end{align*}