Solve Input Math Problem: y``+y`+y=r(t)

[asdf1]

y`` +y`+y=r(t)
why's r(t) the input and not t?

 

[marlon]

y`` +y`+y=r(t)
why's r(t) the input and not t?

Because the right hand side of that equation denotes a function of t.

r(t) could be t but it can also be every other function that depends on t.

Basically, r(t) is the most general form to denote "a function of t"

marlon

 

[HallsofIvy]

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'+ 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".

(Edited- thanks, Marlon.)

 

[marlon]

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".

The differential operator is not y''+y' but y''+y'+y

marlon

 

[asdf1]

thank you very much!