Is This Fourth Order DE Nonlinear?

[bengaltiger14]

Is this DE nonlinear?

Homework Statement

Determine the order and if this equation is Linear or Nonlinear.

3(d4x/dt4) + 4(dx/dt) + 9x = 3cos(3t)

The d4x is a forth order derivative. Sorry for the messiness.

Ok, this is a 4th order DE. I think it is nonlinear because of the two products (multiplying 4 time the derivative and 4 times the other derivative).

Also, the 3cos(3t) has no bearing on this because t is independent right? If the t was a y, that would cause nonlinearness.

Am I right on all this?

 

[NoMoreExams]

Define linear DE

 

[bengaltiger14]

A linear differential equation is one in which the derivative has no function of itself (e^y, cosy, ln(y)). That is if I was differentiating with respect to y.

 

[NoMoreExams]

http://en.wikipedia.org/wiki/Linear_differential_equation sure seems like you can multiply derivatives (of any magnitude) by constants and it won't matter?

 

[bengaltiger14]

Ok.. So my equation is Linear. But you cannot have, 3a*y'. This product will make it nonlinear.

 

[NoMoreExams]

What's a?