# Solving a 1st order nonlinear ODE

Help with solving this nonlinear ODE analytically:

$$\frac{dx}{dt}=4x^2-16$$

I tried doing some kinds of variable substitutions but I was going nowhere.

The solution given is: $$\frac{2(x_0e^{16t}+x_0-2e^{16t}+2)}{-x_0e^{16t}+x_0+2e^{16t}+2}$$

Given equation is

$$x'\:-4x^2+16=0$$

$$\Rightarrow \frac{1}{x^2-4}x'\:=4$$

So it is the first-order ODE of the form

$$N(x)x'=M(t)$$ where $$N(x)=\frac{1}{x^2-4}$$ and $$M(t)=4$$

I hope you know how to solve Separable Equations (simple integration).

For hint check this

Hint.

Try to solve

$$\frac{dx}{(2x-4)(2x+4)} = dt$$