I've been studying Euler's method to approximate a solution to a differential equation in an algorithm class.
I faced a weird differential equation in a mathematics exercise, and I wanted to know if Euler method was applicable to it. This equation is : $$f(x)=\int_0^{ax}f(t)dt + g(x)$$ $g$ being a known function (for which I know the derivative).
I've tried to transform the equation a bit, and I'm getting : $$\frac{df}{dt}(t)=af(at)+\frac{dg}{dt}(t)$$
However, in my lecture, Euler's method is applicable to $$\frac{du}{dt}(x)=f(x,u(x))$$ And here, my equation depends on $f(at)$ and not $f(t)$. Is Euler method still applicable?
If not, is there any other method I could use?