60.2.254 problem 830

Internal problem ID [10841]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 830
Date solved : Monday, January 27, 2025 at 10:12:36 PM
CAS classification : [_rational]

\begin{align*} y^{\prime }&=\frac {y \left (x -y\right )}{x \left (x -y-y^{3}-y^{4}\right )} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 38

dsolve(diff(y(x),x) = y(x)*(x-y(x))/x/(x-y(x)-y(x)^3-y(x)^4),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (2 \,{\mathrm e}^{4 \textit {\_Z}}+3 \,{\mathrm e}^{3 \textit {\_Z}}-6 \,{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+6 c_{1} {\mathrm e}^{\textit {\_Z}}+6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+6 x \right )} \]

✓ Solution by Mathematica

Time used: 0.308 (sec). Leaf size: 38

DSolve[D[y[x],x] == ((x - y[x])*y[x])/(x*(x - y[x] - y[x]^3 - y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {1}{3} y(x)^3-\frac {y(x)^2}{2}-\frac {x}{y(x)}-\log (y(x))+\log (x)-1=c_1,y(x)\right ] \]