4.12.37 \(a+2 x^3 y(x) y'(x)+3 x^2 y(x)^2=0\)

ODE
\[ a+2 x^3 y(x) y'(x)+3 x^2 y(x)^2=0 \] ODE Classification

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

Book solution method
Exact equation

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

\[\left \{\left \{y(x)\to -\frac {\sqrt {c_1-a x}}{x^{3/2}}\right \},\left \{y(x)\to \frac {\sqrt {c_1-a x}}{x^{3/2}}\right \}\right \}\]

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

\[ \left \{ {\frac {a}{{x}^{2}}}-{\frac {{\it \_C1}}{{x}^{3}}}+ \left (y \relax (x ) \right ) ^{2}=0 \right \} \] 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