Internal problem ID [8521]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 185.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
\[ \boxed {x^{7} y^{\prime }+2 \left (x^{2}+1\right ) y^{3}+5 x^{3} y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(x^7*diff(y(x),x) + 2*(x^2+1)*y(x)^3 + 5*x^3*y(x)^2=0,y(x), singsol=all)
\[ c_{1} +\frac {x}{{\left (\left (\frac {1}{x}+\frac {x^{2}}{y \left (x \right )}\right )^{2}+1\right )}^{\frac {1}{4}}}+\frac {\left (x^{3}+y \left (x \right )\right ) \operatorname {hypergeom}\left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (x^{3}+y \left (x \right )\right )^{2}}{y \left (x \right )^{2} x^{2}}\right )}{2 y \left (x \right ) x} = 0 \]
✓ Solution by Mathematica
Time used: 0.319 (sec). Leaf size: 123
DSolve[x^7*y'[x] + 2*(x^2+1)*y[x]^3 + 5*x^3*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [c_1=\frac {\frac {1}{2} \sqrt [4]{1-\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2} \left (\frac {i x^2}{y(x)}+\frac {i}{x}\right ) \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {5}{4},\frac {3}{2},\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {i x^2}{y(x)}+\frac {i}{x}\right )^2}},y(x)\right ] \]