Buxoro davlat universiteti fizika-matematika fakulteti "matematika" kafedrasi

General Solution of a Differential Equation

1. 
   A differential equation is an equation involving a differentiable function and one or more of its derivatives. For instance,
   

Differential equation

is a differential equation. A function y=f(x) is a solution of a differential equation if the equation is satisfied when and its derivatives are replaced f(x) by and its derivatives. For example,

Solution of differential equation

is a solution of the differential equation shown above. To see this, substitute for and

in the orginal equation.

Substitute for and

General solution

where is a real number, is a solution of the equation. This family of solutions is called the general solution of the differential equation.

Albatta, bu masalani tushunish differensial tenglamalar fanini va ingliz tilini yaxshi bilganlarlarga umuman qiyinchilik tug’dirmaydi. Bunda birinchi tartibli oddiy diferensial tenglamaning umumiy yechimi haqida so’z yuritilgan.