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^x-e^-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^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.

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