What is the solution for (dy)/(dx)=(8xsqrt(4-y^2))/(sqrt(4-y^2)) ?

The solution for (dy)/(dx)=(8xsqrt(4-y^2))/(sqrt(4-y^2)) is y=4x^2+c_{1}

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(dy)/(dx)=(8xsqrt(4-y^2))/(sqrt(4-y^2))

\frac{d y}{d x} = \frac{8 x 4 - y ^{2}}{4 - y ^{2}}

y = 4 x^{2} + c_{1}

Solution steps

\frac{d y}{d x} = \frac{8 x 4 - y ^{2}}{4 - y ^{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{8 x 4 - y ^{2}}{4 - y ^{2}}

Simplify

y^{^{'}} (x) = 8 x

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

then

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

y = \int 8 x d x

\int 8 x d x = 4 x^{2} + c_{1}

y = 4 x^{2} + c_{1}

\int \frac{1}{( 1 + sin ( x ) )} d x

x^{2} - 4, - 2 x - 3, - 1, 0

\int (3 x - 2) \cdot e^{- x} d x

x \to 5 + lim (5 - x)

\frac{d}{d x} (\frac{1}{( x + 3 )})

What is the solution for (dy)/(dx)=(8xsqrt(4-y^2))/(sqrt(4-y^2)) ?
The solution for (dy)/(dx)=(8xsqrt(4-y^2))/(sqrt(4-y^2)) is y=4x^2+c_{1}