Internal problem ID [9305]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 971.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]
\[ \boxed {y^{\prime }-\frac {\left (y x +1\right )^{3}}{x^{5}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 70
dsolve(diff(y(x),x) = (x*y(x)+1)^3/x^5,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-2+x^{3} \left (\tan \left (\operatorname {RootOf}\left (18 x^{3} \left (-\frac {1}{x^{6}}\right )^{\frac {2}{3}}+6 \textit {\_Z} \sqrt {3}-3 \ln \left (3\right )+\ln \left (\left (\sqrt {3}\, \sin \left (\textit {\_Z} \right )+3 \cos \left (\textit {\_Z} \right )\right )^{6}\right )-18 c_{1} \right )\right ) \sqrt {3}+1\right ) \left (-\frac {1}{x^{6}}\right )^{\frac {1}{3}}}{2 x} \]
✓ Solution by Mathematica
Time used: 0.23 (sec). Leaf size: 157
DSolve[y'[x] == (1 + x*y[x])^3/x^5,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\arctan \left (\frac {\frac {2 \left (\frac {3}{x^3}+\frac {3 y(x)}{x^2}\right )}{3 \sqrt [3]{-\frac {1}{x^6}}}-1}{\sqrt {3}}\right )}{\sqrt {3}}+\frac {1}{3} \log \left (\frac {\frac {3}{x^3}+\frac {3 y(x)}{x^2}}{3 \sqrt [3]{-\frac {1}{x^6}}}+1\right )-\frac {1}{6} \log \left (\frac {\left (\frac {3}{x^3}+\frac {3 y(x)}{x^2}\right )^2}{9 \left (-\frac {1}{x^6}\right )^{2/3}}-\frac {\frac {3}{x^3}+\frac {3 y(x)}{x^2}}{3 \sqrt [3]{-\frac {1}{x^6}}}+1\right )=-\left (-\frac {1}{x^6}\right )^{2/3} x^3+c_1,y(x)\right ] \]