Internal problem ID [8336]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 756.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x^{3} y+x^{6}+x^{2} y^{2}+y^{3}}{x^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 37
dsolve(diff(y(x),x) = (2*x^3*y(x)+x^6+x^2*y(x)^2+y(x)^3)/x^4,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-3+29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right )\right ) x^{2}}{9} \]
✓ Solution by Mathematica
Time used: 0.133 (sec). Leaf size: 95
DSolve[y'[x] == (x^6 + 2*x^3*y[x] + x^2*y[x]^2 + y[x]^3)/x^4,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {\frac {3 y(x)}{x^4}+\frac {1}{x^2}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^6}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {1}{9} 29^{2/3} \left (\frac {1}{x^6}\right )^{2/3} x^5+c_1,y(x)\right ] \]