Question

does anyone know how to solve this ?
given an equation : y(t) = 5x^2 (t) - 4 dy/dt
a. proof that the system is linear or nonlinear
b. proof that the system is time invariant or time variant

Answer 1

If it's linear, y(3)-y(2) should be equal to y(2)-y(1).
If it's time variant, y(1) and y(2) should be different.

Answer 2

@Preetha can you check my answer? :)

Answer 3

t is independent variable ?

Answer 4

do you mean 4y'(t)+y(t)=5x^2(t) ?

Answer 5

It looks linear. You could probably solve this by finding the integrating factor.

Answer 6

can u guide me ?

Answer 7

Do you know about integrating factors?

Answer 8

\(\sf 5x^2-4\frac{dy}{dt}\) = y(t) Is that what you're given?

Answer 9

yuph

Answer 10

Well, I don't think (From what you have up there) you need to solve. It is just asking you to prove that the system is \(linear\). Which it is. A linear function has the property that its response to the sum of two inputs is the sum of the responses to each input separately. Very similar to the whole superposition princciple

Answer 11

Another test you can do is to check if doubling the input doubles the output. that often tells you that a system is linear.

Answer 12

Also, you have too many variables to solve. You have x(t), \(\sf \frac{dy}{dt}\), and y(t)?

Answer 13

That should also imply something else.