Help with solving this nonlinear ODE analytically:


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


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

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



Try to solve

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


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