How can I solve this first order DE with initial value y(0)=3^(1/2)/2?

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The discussion focuses on solving the first-order differential equation given by the equation dx/(1-y^2)^(1/2) = dy/(1-x^2)^(1/2) with the initial condition y(0) = 3^(1/2)/2. The user correctly separated the variables and integrated, resulting in the equation sin^-1(x) + C = sin^-1(y). To find the constant C, the user is advised to substitute the initial values x = 0 and y = 3^(1/2)/2 into the equation and solve for C, which will lead to the complete solution of the differential equation.

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Eastonc2
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The problem:

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

y(0)=3^(1/2)/2

My attempt:

I separated the variables and integrated, and came up with

sin^-1(x)+c=sin^-1(y)

This is where i am stuck. any suggestions? did I run astray anywhere?
 
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You seem to be on the right track. Now given the initial value, plug in 0 for x and 3^(1/2)/2 for y and solve for C. You should take it from there.
 

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