4.1.11 \(y'(x)=a x^n y(x)\)

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

\[ \left \{ y \relax (x ) ={\it \_C1}\,{{\rm e}^{{\frac {{x}^{n+1}a}{n+1}}}} \right \} \] 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)