Nonlinear first order differential equation

[dreamwere]

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 approach 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.

 

[vela]

That equation is separable.

 

[HallsofIvy]

As vela said, the equation separable:

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

It might help to factor the "G" out leaving
\frac{1}{G}\frac{dx}{\frac{R}{G}x^2+ 1}= dt
and recognize the integral as an "arctangent".

 

[dreamwere]

Thank you done.

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