You get a bonus - 1 coin for daily activity. Now you have 1 coin

4.1.1. General concepts of first order differential equations

Lecture



A first-order differential equation has the form F ( x, y, y ' ) or y' = f ( x, y ) , where y is an unknown function of the variable x .

The function y = φ ( x ) is called the solution of a differential equation if, by substituting y = φ ( x ) and its derivative into this equation, an identity is obtained.

The set of all solutions of a differential equation is called a general solution. It is represented as some function y = φ ( x, c ) ( c is a constant). With proper selection of the constant c, the function φ ( x, c ) defines any particular solution.

The task of finding a solution to a differential equation that satisfies the initial condition y ( x 0 ) = y 0 is called the Cauchy problem.

created: 2014-09-20
updated: 2021-03-13
132490



Rating 9 of 10. count vote: 2
Are you satisfied?:



Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Mathematical analysis. Differential equations

Terms: Mathematical analysis. Differential equations