ODE
\[ y'(x)=a x^n y(x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.00608288 (sec), leaf count = 22
\[\left \{\left \{y(x)\to c_1 e^{\frac {a x^{n+1}}{n+1}}\right \}\right \}\]
Maple ✓
cpu = 0.093 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{n+1}a}{n+1}}}} \right \} \] Mathematica raw input
DSolve[y'[x] == a*x^n*y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^((a*x^(1 + n))/(1 + n))*C[1]}}
Maple raw input
dsolve(diff(y(x),x) = a*x^n*y(x), y(x),'implicit')
Maple raw output
y(x) = _C1*exp(x^(n+1)/(n+1)*a)