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

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

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

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

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

Solution steps

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

Isolate

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}

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