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