12.5.41 problem 38

Internal problem ID [1665]
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
Date solved : Monday, January 27, 2025 at 05:22:57 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {x^{2}+y x +y^{2}}{y x} \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 22

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

\[ y = x \left (-\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_1 -1}}{x}\right )-1\right ) \]

✓ Solution by Mathematica

Time used: 3.983 (sec). Leaf size: 31

DSolve[D[y[x],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*}