ODE
\[ x^7 y(x) y'(x)=5 x^3 y(x)+2 \left (x^2+1\right ) \] ODE Classification
[_rational, [_Abel, `2nd type`, `class B`]]
Book solution method
Abel ODE, Second kind
Mathematica ✓
cpu = 0.865411 (sec), leaf count = 98
\[\text {Solve}\left [c_1=\frac {\frac {i \left (x^3 y(x)+1\right ) \sqrt [4]{x^4 y(x)^2+\frac {1}{x^2}+2 x y(x)+1} \, _2F_1\left (\frac {1}{2},\frac {5}{4};\frac {3}{2};-\frac {\left (y(x) x^3+1\right )^2}{x^2}\right )}{2 x}+i x}{\sqrt [4]{-\frac {\left (x^3 y(x)+1\right )^2}{x^2}-1}},y(x)\right ]\]
Maple ✓
cpu = 0.045 (sec), leaf count = 96
\[\left [\textit {\_C1} +\frac {-\frac {\left (1+x^{3} y \left (x \right )\right ) \hypergeom \left (\left [\frac {1}{2}, \frac {5}{4}\right ], \left [\frac {3}{2}\right ], -\frac {\left (1+x^{3} y \left (x \right )\right )^{2}}{x^{2}}\right ) \left (\frac {x^{6} y \left (x \right )^{2}+2 x^{3} y \left (x \right )+x^{2}+1}{x^{2}}\right )^{\frac {1}{4}}}{x}-2 x}{\left (\frac {x^{6} y \left (x \right )^{2}+2 x^{3} y \left (x \right )+x^{2}+1}{x^{2}}\right )^{\frac {1}{4}}} = 0\right ]\] Mathematica raw input
DSolve[x^7*y[x]*y'[x] == 2*(1 + x^2) + 5*x^3*y[x],y[x],x]
Mathematica raw output
Solve[C[1] == (I*x + ((I/2)*Hypergeometric2F1[1/2, 5/4, 3/2, -((1 + x^3*y[x])^2/x^2)]*(1 + x^3*y[x])*(1 + x^(-2) + 2*x*y[x] + x^4*y[x]^2)^(1/4))/x)/(-1 - (1 + x^3*y[x])^2/x^2)^(1/4), y[x]]
Maple raw input
dsolve(x^7*y(x)*diff(y(x),x) = 2*x^2+2+5*x^3*y(x), y(x))
Maple raw output
[_C1+(-(1+x^3*y(x))/x*hypergeom([1/2, 5/4],[3/2],-(1+x^3*y(x))^2/x^2)*((x^6*y(x)^2+2*x^3*y(x)+x^2+1)/x^2)^(1/4)-2*x)/((x^6*y(x)^2+2*x^3*y(x)+x^2+1)/x^2)^(1/4) = 0]