Question

how we build differential equation ?

Answer 1

A differential equation is a mathematical expression that relates functions with their variables and their own derivatives of any order.

Examples:
\[f(x)=x \cdot f'(x) \\
e^x=4\cdot f(x) + f'(x) \\
2 \cdot \sin(x) +f'(x)=0.2 \cdot f(x)^2 + f(x) \\
3 \cdot f(x,y)^2 = \frac{\partial f }{\partial x} + \frac{\partial^3 f }{\partial y^3}
\]
definition of the derivative:
\[f' (x) = \lim_{\Delta x \rightarrow 0} \frac{f(x+ \Delta x) - f(x)}{\Delta x}\]