ODE
\[ y'(x)=a x^n y(x) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.163613 (sec), leaf count = 22
\[\left \{\left \{y(x)\to c_1 e^{\frac {a x^{n+1}}{n+1}}\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 19
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {x^{n +1} a}{n +1}}\right ]\] 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))
Maple raw output
[y(x) = _C1*exp(x^(n+1)/(n+1)*a)]