Steps to solve this differential equation

[xmenus]

Hi ,
Can anyone help me on this problem please?!
Answer is given but i want to know steps to come to it, i think i tried a lot to solve it but i couldn't come to the given result.
Thanks to all

 

[tiny-tim]

hi xmenus! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[xmenus]

Here's the link of doc..I think i tried loop method and many other forms but... here i just showed the analogy i tried but i couldn't come to the result.(First circuit is different one)
I took an other example just to show or ask if the other circuit can be solved with the same analogy?!

https://www.dropbox.com/sh/7g4vmpl4uhjbyl4/wwNdGrKm5o

 

[tiny-tim]

it's rather difficult to read

anyway, what is D ? ​

 

[psparky]

That's a tough circuit you posted for finding a differential equation.

Don't know for sure...but perhaps a node analysis on the upper right hand node? Current in equal current out sort of thing.

Using SL and 1/(SC) may simplify things as well.

 

[xmenus]

I = C(d/dt)V = CDV

If I am not taking a lot from your time i uploaded the source book.
https://www.dropbox.com/sh/yz2ynkgd1nrwh8r/ItldhMI6SX

It's Chapter 6, problems are excatly at page 299.Solutions at page 302.
Thanks a lot

 

[tiny-tim]

I took an other example just to show or ask if the other circuit can be solved with the same analogy?!

ah, D = d/dt !

ok, you've replaced C and R₃ (in series) by an impedance Z₁

(btw, wouldn't Z₃ be an easier name to keep track of? )

then you've replaced R₂ and Z₁ (in parallel) by Z_e

but then you've stopped (presumably you're going to replace L and Z_e, then replace that and R₁?)

well, that looks fine so far …

what's the difficulty?​

 

[xmenus]

The problem is that it's not working like that.I can't come to the result, i don't know!?

 

[tiny-tim]

but you stopped, you only got as far as Z_e

 

[xmenus]

No,actually i worked on it till to the end but the result i got is not like the given one.
You are right, i didnt post other steps,but on that way it didnt work!

 

[tiny-tim]

we can't comment on why it didn't work unless you show us what you did

 

[xmenus]

Finally,after many attempts, i solved it :D !

I might post the solution so anyone can find it useful maybe.
Thank you a lot anyway,and thank for your time!

 

[xmenus]

Solution is in .pdf file.

Regards