Internal problem ID [8374]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 794.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x \left (-1+y+x^{2} y^{3}+y^{4} x^{3}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 191
dsolve(diff(y(x),x) = y(x)/x/(-1+y(x)+x^2*y(x)^3+y(x)^4*x^3),y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = -\frac {\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}+2 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}}+4}{6 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}} x} \\ y \relax (x ) = \frac {\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}+4-4 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}}-i \sqrt {3}\, \left (-\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}+4\right )}{12 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}} x} \\ y \relax (x ) = \frac {\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}+4-4 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}}+i \sqrt {3}\, \left (-\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}+4\right )}{12 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}} x} \\ -y \relax (x )+\int _{}^{x y \relax (x )}\frac {1}{\textit {\_a} \left (\textit {\_a}^{3}+\textit {\_a}^{2}+1\right )}d \textit {\_a} -c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 67
DSolve[y'[x] == y[x]/(x*(-1 + y[x] + x^2*y[x]^3 + x^3*y[x]^4)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 y(x)^3+\text {$\#$1}^2 y(x)^2+1\&,\frac {\text {$\#$1} y(x) \log (x-\text {$\#$1})+\log (x-\text {$\#$1})}{3 \text {$\#$1} y(x)+2}\&\right ]+y(x)-\log (x)=c_1,y(x)\right ] \]