calculus differential equation
posted by malcolm .
Find in implicit form the general solution of differential equation dy/dx=2(e^x-e^-x)/y^2(e^x+e^-x)^4 with (y>0). I know this requires a seperation of variables but I beyond that I am confused by how.Thanks.
dy/dx=2(first )/y^2 (second)
so lets look at the right side.
factor out e^-x
denominator(factor out e^-4x)
so you are left on the right side:
2*e^3x(e^2x -1)/(e^2x+1) dx
or = 2(e^5x)/(e^2x+1) dx + 2e^3x/(e^2x+2) dx
thanks Bob much appreciated. Do I then take the integral of the last line? And is the left hand side 1/3y^3 (from y^)? I do not know how this fits together. Thanks for any further help