What is the solution for (dy)/(dx)= 1/(sqrt(1-x^2))-1/(sqrt(x)) ?

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

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

\frac{d y}{d x} = \frac{1}{1 - x ^{2}} - \frac{1}{x}

y = arcsin (x) - 2 x + c_{1}

Solution steps

\frac{d y}{d x} = \frac{1}{1 - x ^{2}} - \frac{1}{x}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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

then

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

y = \int \frac{1}{1 - x ^{2}} - \frac{1}{x} d x

\int \frac{1}{1 - x ^{2}} - \frac{1}{x} d x = arcsin (x) - 2 x + c_{1}

y = arcsin (x) - 2 x + c_{1}

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