I was going over some common practices for solving ODE's today, and the following question came to mind:
Can we solve a "Differential Equation" of the form $\int {af(x)dx} + bf(x) = c$? I know it technically isn't a D.E, but I don't know a better term for it.
That's when the notation of "$f^{-1}(x)$", the -1st derivative of $f$, and the first antiderivative of $f$.
With this notation, wouldn't one be able to apply the Laplace Transform and solve given some initial conditions?