Expii

Solving Anti-Derivative Equations - Expii

Perhaps the simplest differential equation is the anti-derivative equation, $$y'(x) = f(x)$$, where $$f$$ is a given function of $$x$$. By the FTC, the general solution is $$y(x) = C + \int_0^x f(t)\,dt$$, where $$C = y(0)$$, the constant of integration, is determined by the initial conditions (or sometimes other data).