# 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.

Staff Emeritus
Homework Helper
That equation is separable.

Homework Helper
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.