4.4.5 \(x y'(x)=a y(x)\)

ODE
\[ x y'(x)=a y(x) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.00302576 (sec), leaf count = 11

\[\left \{\left \{y(x)\to c_1 x^a\right \}\right \}\]

Maple
cpu = 0.004 (sec), leaf count = 9

\[ \left \{ y \relax (x ) ={\it \_C1}\,{x}^{a} \right \} \] Mathematica raw input

DSolve[x*y'[x] == a*y[x],y[x],x]

Mathematica raw output

{{y[x] -> x^a*C[1]}}

Maple raw input

dsolve(x*diff(y(x),x) = a*y(x), y(x),'implicit')

Maple raw output

y(x) = _C1*x^a