17-Peridot

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Nonlinear 1°ord differential equation

Hi everybody,
how can I solve this equation?

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

Thanks
Bye

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Best answer by AlanStevens

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

Alan

23-Emerald IV

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

23-Emerald IV

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.

Success!
Luc

25-Diamond I

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

Author

17-Peridot

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

25-Diamond I

From Mathcad's documentation of "odesolve":

The ODE must be linear in its highest derivative term,

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