4.12.37 $a+2x^{3}y(x)y^{\prime }(x)+3x^{2}y(x{)}^2=0$

ODE
$$a+2x^{3}y(x)y^{\prime }(x)+3x^{2}y(x{)}^2=0$$ ODE Classification

[[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

Book solution method
Exact equation

Mathematica ✓
cpu = 0.00846131 (sec), leaf count = 44

$$\{\{y(x)\to -\frac{\sqrt{c_1-ax}}{x^{3/2}}\},\{y(x)\to \frac{\sqrt{c_1-ax}}{x^{3/2}}\}\}$$

Maple ✓
cpu = 0.005 (sec), leaf count = 19

$$\{\frac{a}{x^2}-\frac{\mathit{\_}\mathit{C}\mathit{1}}{x^3}+{\left(y\left(x\right)\right)}^2=0\}$$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> -(Sqrt[-(a*x) + C[1]]/x^(3/2))}, {y[x] -> Sqrt[-(a*x) + C[1]]/x^(3/2)}
}

Maple raw input

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

Maple raw output

1/x^2*a-1/x^3*_C1+y(x)^2 = 0