60.2.192 problem 768

Internal problem ID [10779]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 768
Date solved : Monday, January 27, 2025 at 09:44:01 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {y \left (y+1\right )}{x \left (-y-1+y x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 26

dsolve(diff(y(x),x) = y(x)*(y(x)+1)/x/(-y(x)-1+x*y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.273 (sec). Leaf size: 72

DSolve[D[y[x],x] == (y[x]*(1 + y[x]))/(x*(-1 - y[x] + x*y[x])),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{-\frac {2 x y(x)+y(x)+1}{\sqrt [3]{2} ((x-1) y(x)-1)}}\frac {1}{K[1]^3-\frac {3 K[1]}{2^{2/3}}+1}dK[1]+\frac {1}{9} 2^{2/3} \left (\frac {1}{x}+\log (x)-1\right )=c_1,y(x)\right ] \]