Nonlinear 1o Order D.E.

  • Thread starter pvgomes07
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Hello!!

I am taking a self study diff e course, and I have run into a problem with no one to ask for help.
Here is the problem:

d/dt [ h^3(t) + 3h(t)^2 + 3h(t) ] = q(t)

h(t) is output.
q(t) is input.

is this Nonlinear First Order Differential Equation.
But I could not expand to Taylor Series for linearization... :/

I'm trying to find the transfer function.

Thanks!
 

Answers and Replies

  • #2
HallsofIvy
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It should be basic Calculus that
[tex]\frac{d}{dx}(h^3+ 3h^2+ 3h)= q(t)[/tex]
[tex] 3h^2\frac{dh}{dt}+ 6h\frac{dh}{dt}+ 3\frac{dh}{dt}= (3h^2+ 6h+ 3)\frac{dh}{dt}= q(t)[/tex]
Now what is the linearization of that?
 
  • #3
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Hello!!

I am taking a self study diff e course, and I have run into a problem with no one to ask for help.
Here is the problem:

d/dt [ h^3(t) + 3h(t)^2 + 3h(t) ] = q(t)

h(t) is output.
q(t) is input.

is this Nonlinear First Order Differential Equation.
But I could not expand to Taylor Series for linearization... :/

I'm trying to find the transfer function.

Thanks!
Maybe this will help:

h3 + 3 h2 + 3h = (h +1)3 -1
 
  • #4
798
34
Hi !
Why not imtegrate it first ?
 

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  • #5
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Hi !
Why not imtegrate it first ?
Yeah! Thank you very much!
:)
 

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