ODE
\[ x^7 y'(x)+5 x^3 y(x)^2+2 \left (x^2+1\right ) y(x)^3=0 \] ODE Classification
[_rational, _Abel]
Book solution method
Abel ODE, First kind
Mathematica ✓
cpu = 0.603648 (sec), leaf count = 106
\[\text {Solve}\left [c_1=\frac {\frac {i \sqrt [4]{\frac {x^4}{y(x)^2}+\frac {1}{x^2}+\frac {2 x}{y(x)}+1} \left (x^3+y(x)\right ) \, _2F_1\left (\frac {1}{2},\frac {5}{4};\frac {3}{2};-\frac {\left (x^3+y(x)\right )^2}{x^2 y(x)^2}\right )}{2 x y(x)}+i x}{\sqrt [4]{-\frac {\left (x^3+y(x)\right )^2}{x^2 y(x)^2}-1}},y(x)\right ]\]
Maple ✓
cpu = 0.039 (sec), leaf count = 63
\[\left [\textit {\_C1} +\frac {x}{\left (\left (\frac {1}{x}+\frac {x^{2}}{y \left (x \right )}\right )^{2}+1\right )^{\frac {1}{4}}}+\frac {\left (x^{3}+y \left (x \right )\right ) \hypergeom \left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (x^{3}+y \left (x \right )\right )^{2}}{x^{2} y \left (x \right )^{2}}\right )}{2 y \left (x \right ) x} = 0\right ]\] Mathematica raw input
DSolve[5*x^3*y[x]^2 + 2*(1 + x^2)*y[x]^3 + x^7*y'[x] == 0,y[x],x]
Mathematica raw output
Solve[C[1] == (I*x + ((I/2)*Hypergeometric2F1[1/2, 5/4, 3/2, -((x^3 + y[x])^2/(x^2*y[x]^2))]*(1 + x^(-2) + x^4/y[x]^2 + (2*x)/y[x])^(1/4)*(x^3 + y[x]))/(x*y[x]))/(-1 - (x^3 + y[x])^2/(x^2*y[x]^2))^(1/4), y[x]]
Maple raw input
dsolve(x^7*diff(y(x),x)+5*x^3*y(x)^2+2*(x^2+1)*y(x)^3 = 0, y(x))
Maple raw output
[_C1+x/((1/x+x^2/y(x))^2+1)^(1/4)+1/2*(x^3+y(x))*hypergeom([1/2, 5/4],[3/2],-(x^3+y(x))^2/x^2/y(x)^2)/y(x)/x = 0]