What is the solution for (dy)/(dx)+((1-y^2)/(1-y^2))^{1/2}=0 ?

The solution for (dy)/(dx)+((1-y^2)/(1-y^2))^{1/2}=0 is y=-x+c_{1}

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(dy)/(dx)+((1-y^2)/(1-y^2))^{1/2}=0

\frac{d y}{d x} + (\frac{1 - y ^{2}}{1 - y ^{2}})^{\frac{1}{2}} = 0

y = - x + c_{1}

Solution steps

\frac{d y}{d x} + (\frac{1 - y ^{2}}{1 - y ^{2}})^{\frac{1}{2}} = 0

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) + (\frac{1 - y ^{2}}{1 - y ^{2}})^{\frac{1}{2}} = 0

Isolate

y^{'} (x) : y^{'} (x) = - 1

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int - 1 d x

\int - 1 d x = - x + c_{1}

y = - x + c_{1}

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What is the solution for (dy)/(dx)+((1-y^2)/(1-y^2))^{1/2}=0 ?
The solution for (dy)/(dx)+((1-y^2)/(1-y^2))^{1/2}=0 is y=-x+c_{1}