60.2.217 problem 793

Internal problem ID [10804]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 793
Date solved : Monday, January 27, 2025 at 10:01:04 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

\[ y = \frac {\operatorname {LambertW}\left (-\frac {2 \left (x -1\right ) {\mathrm e}^{3 c_{1} -1}}{x}\right )}{x -1} \]

✓ Solution by Mathematica

Time used: 1.271 (sec). Leaf size: 111

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

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