Internal problem ID [8565]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 985.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (y x +1\right ) \left (y^{2} x^{2}+y x^{2}+2 y x +1+x +x^{2}\right )}{x^{5}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 43
dsolve(diff(y(x),x) = (x*y(x)+1)*(x^2*y(x)^2+x^2*y(x)+2*x*y(x)+1+x+x^2)/x^5,y(x), singsol=all)
\[ y \relax (x ) = \frac {17 \RootOf \left (162 \left (\int _{}^{\textit {\_Z}}\frac {1}{289 \textit {\_a}^{3}+54 \textit {\_a} -54}d \textit {\_a} \right ) x +3 c_{1} x +2\right ) x -3 x -9}{9 x} \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 103
DSolve[y'[x] == ((1 + x*y[x])*(1 + x + x^2 + 2*x*y[x] + x^2*y[x] + x^2*y[x]^2))/x^5,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {17}{3} \text {RootSum}\left [-17 \text {$\#$1}^3+3 \sqrt [3]{-34} \text {$\#$1}-17\&,\frac {\log \left (\frac {\frac {x+3}{x^3}+\frac {3 y(x)}{x^2}}{\sqrt [3]{34} \sqrt [3]{-\frac {1}{x^6}}}-\text {$\#$1}\right )}{\sqrt [3]{-34}-17 \text {$\#$1}^2}\&\right ]=-\frac {1}{9} 34^{2/3} \left (-\frac {1}{x^6}\right )^{2/3} x^3+c_1,y(x)\right ] \]