Nonlinear first order differential equation

  • Thread starter dreamwere
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  • #1
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Homework Statement



Solve the diferential equation: dx/dt + Rx^2 + G = 0

G constant = 10^18
R constant = 10^-10

Initial conditions x(0) = 10^8


Homework Equations



what aproach to take?

The Attempt at a Solution



First I try to apply bernoulli, but since in this equation I do not have a term x and since also the constat G is different to cero, it was not possible.

Secondly I try to solve in the frequency domain, and using laplace transformation I obtain:

Xs = 2R/s^2 + sx(0) + G

But then, things get complicate trying to convert to time domain for the second and first term becouse the first one implies a delta function in t = 0 and the second one implies a derivations of the inverse transfor of x(0), that is again an impulse sus the derivative of the impulse.

Thank you in advance for taking your time to help me.
 

Answers and Replies

  • #2
vela
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That equation is separable.
 
  • #3
HallsofIvy
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As vela said, the equation separable:

Write it as
[tex]\frac{dx}{Rx^2+ G}= dt[/tex]
and integrate both sides.

It might help to factor the "G" out leaving
[tex]\frac{1}{G}\frac{dx}{\frac{R}{G}x^2+ 1}= dt[/tex]
and recognize the integral as an "arctangent".
 
  • #4
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Thank you done.

Sory for wasting your time, I should try harder before asking.
 

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