Posted by malcolm on Saturday, February 12, 2011 at 12:53pm.
Find in implicit form the general solution of differential equation dy/dx=2(e^xe^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.

calculus differential equation  bobpursley, Saturday, February 12, 2011 at 3:56pm
dy/dx=2(first )/y^2 (second)
y^2 dy=2(first)dx/(second)
so lets look at the right side.
2(e^xe^x)/(e^x+e^x)^4
factor out e^x
numerator: 2e^x(e^2x)
denominator(factor out e^4x)
e^4x (e^2x1)^2
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

calculus differential equation  mike, Tuesday, February 15, 2011 at 12:41pm
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
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