Internal problem ID [9129]
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]
\[ \boxed {y^{\prime }-\frac {y}{x \left (-1+y+y^{3} x^{2}+y^{4} x^{3}\right )}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 209
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 \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {-\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}-4-2 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}}}{6 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {i \sqrt {3}\, \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}-4 i \sqrt {3}+\left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {2}{3}}-4 \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}}+4}{12 \left (116+12 \sqrt {3}\, \sqrt {31}\right )^{\frac {1}{3}} x} \\ y \left (x \right ) &= \frac {-i \left (116+12 \sqrt {93}\right )^{\frac {2}{3}} \sqrt {3}+\left (116+12 \sqrt {93}\right )^{\frac {2}{3}}+4 i \sqrt {3}-4 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}}+4}{12 \left (116+12 \sqrt {93}\right )^{\frac {1}{3}} x} \\ -y \left (x \right )+\int _{}^{x y \left (x \right )}\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: 0.16 (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]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 y(x)^3+\text {$\#$1}^2 y(x)^2+1\&,\frac {\text {$\#$1} y(x) \log (x-\text {$\#$1})+\log (x-\text {$\#$1})}{3 \text {$\#$1} y(x)+2}\&\right ]+y(x)-\log (x)=c_1,y(x)\right ] \]