In this post, I'll introduce about Diffrential Equations.

First-order differential
equations
Reference: Boyce and DiPrima, Chapter 2
The general first-order differential equation for the function 𝑦 = 𝑦(𝑥) is written
as
𝑑𝑦
𝑑𝑥 = 𝑓(𝑥, 𝑦), (2.1)
where 𝑓(𝑥, 𝑦) can be any function of the independent variable 𝑥 and the dependent
variable 𝑦. We first show how to determine a numerical solution of this
equation, and then learn techniques for solving analytically some special forms
of (2.1), namely, separable and linear first-order equations.
2.1 The Euler method
view tutorial
Although it is not always possible to find an analytical solution of (2.1) for
𝑦 = 𝑦(𝑥), it is always possible to determine a unique numerical solution given
an initial value 𝑦(𝑥0) = 𝑦0, and provided 𝑓(𝑥, 𝑦) is a well-behaved function.
The differential equation (2.1) gives us the slope 𝑓(𝑥0, 𝑦0) of the tangent line
to the solution curve 𝑦 = 𝑦(𝑥) at the point (𝑥0, 𝑦0). With a small step…

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