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).