5.41 problem 38

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]]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}+y x +y^{2}}{y x}=0} \end {gather*}

Solution by Maple

Time used: 0.024 (sec). Leaf size: 28

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

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

Solution by Mathematica

Time used: 106.338 (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+\text {ProductLog}\left (-\frac {e^{-1-c_1}}{x}\right )\right ) \\ y(x)\to -x \\ \end{align*}