Internal problem ID [8490]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 910.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-2 x -y+1+x^{2} y^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 42
dsolve(diff(y(x),x) = (-2*x-y(x)+1+x^2*y(x)^2+2*x^3*y(x)+x^4+x^3*y(x)^3+3*x^4*y(x)^2+3*x^5*y(x)+x^6)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {-9 x^{2}+29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right )-3}{9 x} \]
✓ Solution by Mathematica
Time used: 0.169 (sec). Leaf size: 98
DSolve[y'[x] == (1 - 2*x + x^4 + x^6 - y[x] + 2*x^3*y[x] + 3*x^5*y[x] + x^2*y[x]^2 + 3*x^4*y[x]^2 + x^3*y[x]^3)/x,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {3 x^3+3 x^2 y(x)+x}{\sqrt [3]{29} \sqrt [3]{x^3}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {29^{2/3} \left (x^3\right )^{2/3}}{9 x}+c_1,y(x)\right ] \]