4.1   \(y'(x)=a f(x)\)

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

[_quadrature]

Book solution method
Separable ODE, Dependent variable missing

Mathematica
cpu = 0.099971 (sec), leaf count = 19

\[\left \{\left \{y(x)\to \int _1^x a f(K[1]) \, dK[1]+c_1\right \}\right \}\]

Maple
cpu = 0.54 (sec), leaf count = 12

\[ \left \{ y \left ( x \right ) =\int \!af \left ( x \right ) \,{\rm d}x+{\it \_C1} \right \} \] Mathematica raw input

DSolve[y'[x] == a*f[x],y[x],x]

Mathematica raw output

{{y[x] -> C[1] + Integrate[a*f[K[1]], {K[1], 1, x}]}}

Maple raw input

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

Maple raw output

y(x) = Int(a*f(x),x)+_C1