Question #f913b
1 Answer
A simple first ordinary differential equation:
Explanation:
Introduction
Differential equations can be classified essentially on: ordinary and partial. Furthermore, they can be classified into: linear and nonlinear.
Fundamentaly. linear differential equations do not have variables in their coefficients. The simplest example are ordinary differential equations (ODEs).
The general form for linear first order ODEs:
They all have analytical solutions.
A simple Linear ordinary differential equations
Applying the following strategy, we can obtain the solution for any equation of this shape.
Multiply both side by
See that it takes us to conclude:
By basic calculus, we can find:
Moreover, we can conclude that:
By calculus, we can find the solution:
Some words about the solution
It does not matter the initial solution, it will always converge to it; it is a nice property since as long as you give enough time, the system will always come back to the initial state.
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