60.2.242 problem 818

Internal problem ID [10829]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 818
Date solved : Monday, January 27, 2025 at 10:09:36 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} y^{\prime }&=\frac {y}{x \left (-1+y x +x y^{3}+x y^{4}\right )} \end{align*}

Solution by Maple

Time used: 0.026 (sec). Leaf size: 34

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

Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 34

DSolve[D[y[x],x] == y[x]/(x*(-1 + x*y[x] + x*y[x]^3 + x*y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
 
\[ \text {Solve}\left [\frac {y(x)^3}{3}+\frac {y(x)^2}{2}+\frac {1}{x y(x)}+\log (y(x))=c_1,y(x)\right ] \]