What is the solution for (dy)/(dx)= x/(sqrt(1-4x^2)) ?

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

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(dy)/(dx)= x/(sqrt(1-4x^2))

\frac{d y}{d x} = \frac{x}{1 - 4 x ^{2}}

y = - \frac{1}{4} 1 - 4 x^{2} + c_{1}

Solution steps

\frac{d y}{d x} = \frac{x}{1 - 4 x ^{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = \frac{x}{1 - 4 x ^{2}}

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

then

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

y = \int \frac{x}{1 - 4 x ^{2}} d x

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

y = - \frac{1}{4} 1 - 4 x^{2} + c_{1}

\frac{d ^{3}}{d x ^{3}} ((4 x - 3)^{\frac{1}{2}})

\frac{\partial}{\partial y} (2 x + y^{3})

x \to 1 lim (\frac{∣ x - 8 ∣}{x - 8})

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

x \to 4 lim (- \frac{4}{- x + 4})

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