Posted by grace on Thursday, March 24, 2011 at 6:31pm.
find in implicit form, the general solution of the differential equation
dy/dx = 2(e^xe^x)/y^2(e^x+e^x)^4

maths  MathMate, Friday, March 25, 2011 at 10:06pm
The equation is separable.
After inserting missing parentheses, the equation reads:
dy/dx = 2(e^xe^x)/[y^2(e^x+e^x)^4 ]
which can be separated to give:
y^2 dy = 2(e^xe^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.
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