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 = 0.322281 (sec), leaf count = 44
\[\left \{\left \{y(x)\to -\frac {\sqrt {-a x+c_1}}{x^{3/2}}\right \},\left \{y(x)\to \frac {\sqrt {-a x+c_1}}{x^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 36
\[\left [y \left (x \right ) = \frac {\sqrt {\left (-a x +\textit {\_C1} \right ) x}}{x^{2}}, y \left (x \right ) = -\frac {\sqrt {\left (-a x +\textit {\_C1} \right ) x}}{x^{2}}\right ]\] 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))
Maple raw output
[y(x) = 1/x^2*((-a*x+_C1)*x)^(1/2), y(x) = -1/x^2*((-a*x+_C1)*x)^(1/2)]