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asdf1
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y`` +y`+y=r(t)
why's r(t) the input and not t?
why's r(t) the input and not t?
asdf1 said:y`` +y`+y=r(t)
why's r(t) the input and not t?
HallsofIvy said:That's not really mathematics- it's "Engineer speak".
From the point of view of an Engineer, a differential equation is a machine to which you supply an "input" and get an "output". The differential operator y"+ y' is the machine. Whatever function you have on the right hand side is the "input" (which varies with t) and y(t) satisfying the equation is the "output".
In this equation, "y``" represents the second derivative of y, "y`" represents the first derivative of y, and "y" represents the function itself. "r(t)" is a function of time, which is the independent variable.
To solve for y, you will need to use techniques from differential equations. First, you can rearrange the equation to get all the y terms on one side and the r(t) term on the other. Then, you can use methods such as separation of variables or Euler's method to solve for y.
Yes, this equation can be solved analytically using techniques from differential equations. However, the complexity of the solution will depend on the specific form of the function r(t) and the initial conditions for y.
This equation can be used to model various physical phenomena, such as population growth or the motion of a falling object. By determining the function r(t) and initial conditions, this equation can help predict the behavior of a system over time.
As with any mathematical model, there are limitations to using this equation. It may not accurately represent all real-world situations and its predictions may not be accurate in all cases. Additionally, the solution may become more complex for certain forms of r(t) and initial conditions.