Question

find in implicit form, the general solution of the differential equation

dy/dx = 2(e^x-e^-x)/y^2(e^x+e^-x)^4

Answer 1

The equation is separable.
After inserting missing parentheses, the equation reads:

dy/dx = 2(e^x-e^-x)/[y^2(e^x+e^-x)^4 ]
which can be separated to give:

y^2 dy = 2(e^x-e^-x)/(e^x+e^-x)^4 dx
Note that on the right hand side, the numberator is the derivative of the one term of the denominator, which makes for a convenient substitution.
Integrate both sides:
y^3/3 = -2/[3(e^x+e^-x)^3]+C

What's left is to do the algebraic manipulations to yield an explicit form.