(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the separable equation

2. Relevant equations

dy/dx = 1-y^2

3. The attempt at a solution

dy/dx = 1-y^2

1/(1-y^2) dy = dx

[Partial fraction]

A/(1-y) + B/(1+y) = 1/(1-y^2)

A + Ay + B - By = 1

y^1: A - B = 0

y^0: A + B = 1

=> A=B=1/2 =>

(1/2)/(1-y) dy + (1/2)/(1+y) dy = dx

ln|1-y| + ln |1+y| = 2x + C

ln|1-y^2| = 2x + C

1-y^2 = De^(2x)

y = sqrt(1 - De^(2x))

This answer is wrong according to two different books (without explanation) that i have. The correct answer should be

y = (De^(2x) - 1)/(De^(2x) + 1)

Is partial fraction wrong way to go?

Have I made a wrong turn along the way with the algebra?

I do have big problems when i comes to solve nonlinear integrals, a tip along the way would be very appreciated!

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# Is partial fraction wrong way to go?

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