What is the solution for dx=xsqrt(x^2-16)dy ?

The solution for dx=xsqrt(x^2-16)dy is y= 1/4 arcsec(1/4 x)+c_{1}

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dx=xsqrt(x^2-16)dy

d x = x x^{2} - 16 d y

y = \frac{1}{4} arcsec (\frac{1}{4} x) + c_{1}

Solution steps

d x = x x^{2} - 16 d y

Let

y

be the dependent variable. Divide by

d x

1 = x x^{2} - 16 \frac{d y}{d x}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

1 = x x^{2} - 16 y^{^{'}} (x)

Isolate

y^{'} (x) : y^{'} (x) = \frac{1}{x x ^{2} - 16}

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

then

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

y = \int \frac{1}{x x ^{2} - 16} d x

\int \frac{1}{x x ^{2} - 16} d x = \frac{1}{4} arcsec (\frac{1}{4} x) + c_{1}

y = \frac{1}{4} arcsec (\frac{1}{4} x) + c_{1}

x \to 20 lim (10)

\int ((4 + x^{7})^{6} 7 x^{6}) d x

x \to 3 lim (10)

\frac{\partial}{\partial z} (ln (x yz))

\frac{d}{d x} (x^{2} + a^{2})

What is the solution for dx=xsqrt(x^2-16)dy ?
The solution for dx=xsqrt(x^2-16)dy is y= 1/4 arcsec(1/4 x)+c_{1}