4.12.43 $x^{7}y(x)y^{\prime }(x)=5x^{3}y(x)+2(x^2+1)$

ODE
$$x^{7}y(x)y^{\prime }(x)=5x^{3}y(x)+2(x^2+1)$$ ODE Classification

[_rational, [_Abel, `2nd type`, `class B`]]

Book solution method
Abel ODE, Second kind

Mathematica ✓
cpu = 1.16006 (sec), leaf count = 98

$$\text{Solve}[c_1=\frac{i((x^{3}y(x)+1)\sqrt[4]{x^{4}y(x{)}^2+\frac{1}{x^2}+2xy(x)+1}{}_2{F}_1(\frac{1}{2},\frac{5}{4};\frac{3}{2};-\frac{{(y(x)x^3+1)}^2}{x^2})+2x^2)}{2x\sqrt[4]{-\frac{{(x^{3}y(x)+1)}^2}{x^2}-1}},y(x)]$$

Maple ✓
cpu = 0.055 (sec), leaf count = 96

$$\{\mathit{\_}\mathit{C}\mathit{1}+1(-\frac{1+x^{3}y\left(x\right)}{x}{}_2\text{F}{}_1(\frac{1}{2},\frac{5}{4};\frac{3}{2};-\frac{{(1+x^{3}y\left(x\right))}^2}{x^2})\sqrt[4]{\frac{x^6{\left(y\left(x\right)\right)}^2+2x^{3}y\left(x\right)+x^2+1}{x^2}}-2x)\frac{1}{\sqrt[4]{\frac{x^6{\left(y\left(x\right)\right)}^2+2x^{3}y\left(x\right)+x^2+1}{x^2}}}=0\}$$ 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/2)*(2*x^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),'implicit')

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