' 'solution'' integral curve ''f'' ''u'' ''n'' times differentiable ''i'' math f xuu' ldots u n quad x math given two solutions ''u'' called ''extension'' ''v'' math u x v x quad x math solution extension called ''maximal solution'' solution defined '''r''' called ''global solution'' ''general solution'' ''n''th order equation solution containing ''n'' arbitrary independent constants integration ''particular solution'' derived general solution setting constants
Formal science Mathematics Pure mathematics Analysis Ordinary differential equations