##### 4.19.17 $$y'(x) \left (a+b x^2 y(x)^3\right )+a b y(x)^3+x^2 y'(x)^2=0$$

ODE
$y'(x) \left (a+b x^2 y(x)^3\right )+a b y(x)^3+x^2 y'(x)^2=0$ ODE Classiﬁcation

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for $$y'$$

Mathematica
cpu = 0.21782 (sec), leaf count = 49

$\left \{\left \{y(x)\to -\frac {1}{\sqrt {2 b x-2 c_1}}\right \},\left \{y(x)\to \frac {1}{\sqrt {2 b x-2 c_1}}\right \},\left \{y(x)\to \frac {a}{x}+c_1\right \}\right \}$

Maple
cpu = 0.054 (sec), leaf count = 35

$\left [y \left (x \right ) = \frac {1}{\sqrt {2 b x +\textit {\_C1}}}, y \left (x \right ) = -\frac {1}{\sqrt {2 b x +\textit {\_C1}}}, y \left (x \right ) = \frac {a}{x}+\textit {\_C1}\right ]$ Mathematica raw input

DSolve[a*b*y[x]^3 + (a + b*x^2*y[x]^3)*y'[x] + x^2*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(1/Sqrt[2*b*x - 2*C[1]])}, {y[x] -> 1/Sqrt[2*b*x - 2*C[1]]}, {y[x] ->
 a/x + C[1]}}

Maple raw input

dsolve(x^2*diff(y(x),x)^2+(a+b*x^2*y(x)^3)*diff(y(x),x)+a*b*y(x)^3 = 0, y(x))

Maple raw output

[y(x) = 1/(2*b*x+_C1)^(1/2), y(x) = -1/(2*b*x+_C1)^(1/2), y(x) = a/x+_C1]