Through the Laplace transform of the differential equation, the Laplace transform of the system transfer function is the error of the differential equation It must be said that the clean-up is carried out by the government Sorry, I'm missing an inverse word. The inverse Laplace transform of the system transfer function is a differential equation.

Through the Laplace transform of the differential equation, the Laplace transform of the system transfer function is the error of the differential equation It must be said that the clean-up is carried out by the government Sorry, I'm missing an inverse word. The inverse Laplace transform of the system transfer function is a differential equation.

"Laplace transform of system transfer function is differential equation" is wrong!
The transfer function itself is the form of Laplace transform and can't be transformed any more
If we say that "the inverse Laplace transform of the system transfer function is a differential equation", we should say that "after the input R (s) and output C (s) of the system transfer function are added according to the definition, the differential equation is obtained by performing the inverse Laplace transform on both sides of the equation at the same time."

How to transform differential equation and transfer function, transfer function and state space?
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Differential equations can be transformed into transfer functions by Laplace transform. The next one won't be. I haven't seen it yet. To be continued!

The transfer function is obtained by Laplace transform of differential equation. The inverse Laplace transform of system transfer function is the fault of differential equation

The differential equation is an input-output relation, or R-C relation
After the pull transformation, it becomes the R-C relation in the complex frequency domain, from which the transfer function g = C / R can be obtained
In this process, there may be some reductions, that is, zero pole cancellation
Therefore, it cannot be said that all differential equations can be recovered from G
But for the pull inverse transformation of the transfer function g, we can still get a time-domain expression (instead of an equation, because there is no r in it, or r = 1 by default), which is called shock response
That is, the time domain expression of output C when r = Delta (T) or r = 1

Transfer function of RC parallel circuit

In general, the power supply is the input and the required voltage or current is the output. Suppose R and C are in series, the total voltage connected between R and C is the input (i.e. UI), and the voltage on C is the output (i.e. UO). Then, the differential equation is: UI = RC * uo uo uo