4.2.18 \(y'(x)=a x y(x)^2\)

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00574785 (sec), leaf count = 19

\[\left \{\left \{y(x)\to -\frac {2}{a x^2+2 c_1}\right \}\right \}\]

Maple
cpu = 0.004 (sec), leaf count = 17

\[ \left \{ \left (y \relax (x ) \right ) ^{-1}+{\frac {a{x}^{2}}{2}}-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y'[x] == a*x*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> -2/(a*x^2 + 2*C[1])}}

Maple raw input

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

Maple raw output

1/y(x)+1/2*a*x^2-_C1 = 0