- #1

- 21

- 0

I ended up with this PDE:

du/dt + A*u² =C

A and C are constants and U is only function of time.

It looks simple but...

Can someone help me?

Thanks a lot in advance

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- Thread starter kaniello
- Start date

- #1

- 21

- 0

I ended up with this PDE:

du/dt + A*u² =C

A and C are constants and U is only function of time.

It looks simple but...

Can someone help me?

Thanks a lot in advance

- #2

CompuChip

Science Advisor

Homework Helper

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It is a Riccati equation, and indeed it is slightly more tricky than you may initially think.

- #3

- 21

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Thank you so much!! That was a quick answer!

- #4

- 13,194

- 763

Can't you just separate variables ?

- #5

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- #6

- 13,194

- 763

[tex] \frac{du}{dt} = C-Au^2 \Rightarrow \int dt = \int\frac{du}{C-Au^2} \Rightarrow...[/tex]

??

- #7

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tanh⁻1([itex]\sqrt{a/c}[/itex] / (a/c).

I am currently studying the article from CompuChip and reference given there. Probably this is the solution that comes out from the Riccati equation setting q1=0, q0 and q2= const.

- #8

AlephZero

Science Advisor

Homework Helper

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It is a Riccati equation, and indeed it is slightly more tricky than you may initially think.

The Riccati equation is only "tricky" in the general case - for example when C in the OP's equation is replaced by something like [itex]Ct^n[/itex]

As dextercioby said, this special case is straighforward to integrate.

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