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 = 0.00684162 (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 = 0.01 (sec), leaf count = 25

\[ \left \{ \left (y \relax (x ) \right ) ^{-2}-2\,bx-{\it \_C1}=0,y \relax (x ) ={\frac {a}{x}}+{\it \_C1} \right \} \] 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),'implicit')

Maple raw output

1/y(x)^2-2*b*x-_C1 = 0, y(x) = 1/x*a+_C1