Internal problem ID [8356]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 778.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
\[ \boxed {y^{\prime }-\frac {-3 y x^{2}+1+y^{2} x^{6}+y^{3} x^{9}}{x^{3}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x) = (-3*x^2*y(x)+1+y(x)^2*x^6+y(x)^3*x^9)/x^3,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-3+29 \operatorname {RootOf}\left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1} \right )}{9 x^{3}} \]
✓ Solution by Mathematica
Time used: 1.135 (sec). Leaf size: 95
DSolve[y'[x] == (1 - 3*x^2*y[x] + x^6*y[x]^2 + x^9*y[x]^3)/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {3 x^6 y(x)+x^3}{\sqrt [3]{29} \sqrt [3]{x^9}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {29^{2/3} \left (x^9\right )^{2/3}}{9 x^5}+c_1,y(x)\right ] \]