60.2.201 problem 777

Internal problem ID [10788]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 777
Date solved : Monday, January 27, 2025 at 09:44:30 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{\prime }&=\frac {y \left (y+1\right )}{x \left (-y-1+x y^{4}\right )} \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 59

dsolve(diff(y(x),x) = y(x)*(y(x)+1)/x/(-y(x)-1+x*y(x)^4),y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= -1 \\ y &= {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{3 \textit {\_Z}} x -5 x \,{\mathrm e}^{2 \textit {\_Z}}+2 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+7 x \,{\mathrm e}^{\textit {\_Z}}-2 c_{1} x -2 x \textit {\_Z} -3 x +2\right )}-1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.139 (sec). Leaf size: 38

DSolve[D[y[x],x] == (y[x]*(1 + y[x]))/(x*(-1 - y[x] + x*y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
 

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