Internal problem ID [9310]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 976.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
\[ \boxed {y^{\prime }-\frac {y \left (y^{2} x^{7}+y x^{4}+x -3\right )}{x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 70
dsolve(diff(y(x),x) = y(x)/x*(y(x)^2*x^7+y(x)*x^4+x-3),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (-\sqrt {3}\, \ln \left (3\right )-\sqrt {3}\, \ln \left (-\frac {1}{-2+\sqrt {3}\, \sin \left (2 \textit {\_Z} \right )+\cos \left (2 \textit {\_Z} \right )}\right )+\sqrt {3}\, \ln \left (7\right )+3 \sqrt {3}\, c_{1} -2 \sqrt {3}\, x -2 \textit {\_Z} \right )\right )-1}{2 x^{3}} \]
✓ Solution by Mathematica
Time used: 1.135 (sec). Leaf size: 101
DSolve[y'[x] == (y[x]*(-3 + x + x^4*y[x] + x^7*y[x]^2))/x,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {7}{3} \text {RootSum}\left [-7 \text {$\#$1}^3+6 \sqrt [3]{-7} \text {$\#$1}-7\&,\frac {\log \left (\frac {3 x^6 y(x)+x^3}{\sqrt [3]{7} \sqrt [3]{-x^9}}-\text {$\#$1}\right )}{2 \sqrt [3]{-7}-7 \text {$\#$1}^2}\&\right ]=\frac {7^{2/3} \left (-x^9\right )^{2/3}}{9 x^5}+c_1,y(x)\right ] \]