Internal problem ID [1013]
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: 36(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x y y^{\prime }-x^{2}+y x -y^{2}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve(x*y(x)*diff(y(x),x)=x^2-x*y(x)+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (\frac {{\mathrm e}^{-1} {\mathrm e}^{-c_{1}}}{x}\right )-c_{1} -1}+x \]
✓ Solution by Mathematica
Time used: 3.588 (sec). Leaf size: 25
DSolve[x*y[x]*y'[x]==x^2-x*y[x]+y[x]^2,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*}