How do I solve this Nonlinear First Order Differential Equation?

[pvgomes07]

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!

 

[HallsofIvy]

It should be basic Calculus that
$$\frac{d}{dx}(h^3+ 3h^2+ 3h)= q(t)$$
$$3h^2\frac{dh}{dt}+ 6h\frac{dh}{dt}+ 3\frac{dh}{dt}= (3h^2+ 6h+ 3)\frac{dh}{dt}= q(t)$$
Now what is the linearization of that?

 

[Chestermiller]

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

 

[JJacquelin]

Hi !
Why not imtegrate it first ?

 

[pvgomes07]

Hi !
Why not imtegrate it first ?

Yeah! Thank you very much!
:)