Internal problem ID [8556]
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]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (y^{2} x^{7}+y x^{4}+x -3\right )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 57
dsolve(diff(y(x),x) = y(x)/x*(y(x)^2*x^7+y(x)*x^4+x-3),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {3}\, \tan \left (\RootOf \left (-\sqrt {3}\, \ln \left (\frac {\frac {9 \left (\tan ^{2}\left (\textit {\_Z} \right )\right )}{7}+\frac {9}{7}}{\left (\sqrt {3}-3 \tan \left (\textit {\_Z} \right )\right )^{2}}\right )+3 \sqrt {3}\, c_{1}-2 \sqrt {3}\, x -2 \textit {\_Z} \right )\right )-1}{2 x^{3}} \]
✓ Solution by Mathematica
Time used: 0.128 (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]
\[ \text {Solve}\left [-\frac {7}{3} \text {RootSum}\left [-7 \text {$\#$1}^3+6 \sqrt [3]{-7} \text {$\#$1}-7\&,\frac {\log \left (\frac {3 x^6 y(x)+x^3}{\sqrt [3]{7} \sqrt [3]{-x^9}}-\text {$\#$1}\right )}{2 \sqrt [3]{-7}-7 \text {$\#$1}^2}\&\right ]=\frac {7^{2/3} \left (-x^9\right )^{2/3}}{9 x^5}+c_1,y(x)\right ] \]