29.18.32 problem 510

Internal problem ID [5106]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 510
Date solved : Monday, January 27, 2025 at 10:11:35 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 3.336 (sec). Leaf size: 25

DSolve[x y[x] D[y[x],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*}