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Nonlinear 1°ord differential equation

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Pearl

Nonlinear 1°ord differential equation

Hi everybody,
how can I solve this equation?Cattura.JPG

 

I found problems because of the derivative function squared. I need to collect the term derivative not squared...

Thanks
Bye

1 ACCEPTED SOLUTION

Accepted Solutions

Re: Nonlinear 1°ord differential equation

You can turn the non-linear y'(t)^2 + 4y'(t) = 5ty(t) into two simultaneous linear ode's:

 

Non-linearOde.PNG

 

 

 

Alan

View solution in original post

9 REPLIES 9

Re: Nonlinear 1°ord differential equation

Hmm squared.... Seems more like to the 3rd power.

 

You have (y'(t))^2 and mutiply that with 4 y'(t), that gives 4*(y'(t))^3...

 

Do you need a symbolic solution, or can you settle for a numeric approximation.

Either way: what are the initial values? [ y(0), y'(0)]


Luc

Re: Nonlinear 1°ord differential equation

Found it.

 

Try y(t)=+/-(1/8)*sqrt(10)*t^2.

 

The third solution is y(t)=0, but I guess you weren't looking for that.

LM_20180917_NonlinearDE.png

 

Success!
Luc

Re: Nonlinear 1°ord differential equation

Here's a possible workaround for a numerical solution, both Prime and real Mathcad:

B2.png

Re: Nonlinear 1°ord differential equation

I'm so sorry because I wrote "(y'(t)^2) * 4y'(t)" instead of "(y'(t)^2) + 4y'(t)" that it changes a lot...

Re: Nonlinear 1°ord differential equation

From Mathcad's documentation of "odesolve":

The ODE must be linear in its highest derivative term,

 

Re: Nonlinear 1°ord differential equation

Does y(t) describe a physical phenomenon as a function of time? Or is this a made-up DE?

Luc

Re: Nonlinear 1°ord differential equation

You can turn the non-linear y'(t)^2 + 4y'(t) = 5ty(t) into two simultaneous linear ode's:

 

Non-linearOde.PNG

 

 

 

Alan

View solution in original post

Re: Nonlinear 1°ord differential equation

How to find y(0)=1?

z(0)=0, How about z(0)=-4?

Tokoro.

 

Re: Nonlinear 1°ord differential equation

y(0)=1 was an arbitrary choice on my part, as no initial conditions were specified in the original question.

 

z(0)=-4 gives rise to a rapidly decreasing y with time (and with y(0)=1). If this is what is expected from the model then fine! Personally, I think it’s probably safer to stick with z(0)=0.

 

Alan