ODE
\[ y'(x)=a x y(x)^2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.225677 (sec), leaf count = 19
\[\left \{\left \{y(x)\to -\frac {2}{a x^2+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {2}{-a \,x^{2}+2 \textit {\_C1}}\right ]\] 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))
Maple raw output
[y(x) = 2/(-a*x^2+2*_C1)]