09-09-2017, 01:16 PM
A differential equation is any equation that contains one or more derivatives. The simplest differential equation, therefore, is only a problem of habitual integration
y '= f (t).
The solution of the above is, of course, the indefinite integral of f (t), y = F (t) + C, where F (t) is any anti-derivative of f (t) and C is an arbitrary constant. This solution is called the general solution of the differential equation. It is a general form of a set of infinite functions, each of which differs from others by a constant (or more) constant and / or constant coefficients, satisfying the differential equation in question. Each differential equation, if it has a solution, always has infinite functions that satisfy it. All these solutions, which differ from one another by one or more, constant / arbitrary coefficient (s), are given by the formula of the general solution. Additional auxiliary conditions, which could appear as a problem demand, will be required to reduce the set of solutions to one or more specific functions of the general solution formula.
y '= f (t).
The solution of the above is, of course, the indefinite integral of f (t), y = F (t) + C, where F (t) is any anti-derivative of f (t) and C is an arbitrary constant. This solution is called the general solution of the differential equation. It is a general form of a set of infinite functions, each of which differs from others by a constant (or more) constant and / or constant coefficients, satisfying the differential equation in question. Each differential equation, if it has a solution, always has infinite functions that satisfy it. All these solutions, which differ from one another by one or more, constant / arbitrary coefficient (s), are given by the formula of the general solution. Additional auxiliary conditions, which could appear as a problem demand, will be required to reduce the set of solutions to one or more specific functions of the general solution formula.