What is the solution for derivative of x^2-4xy+y^2=4 ?

The solution for derivative of x^2-4xy+y^2=4 is y=2x+sqrt(3x^2+4x+c_{1)},y=2x-sqrt(3x^2+4x+c_{1)}

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derivative of x^2-4xy+y^2=4

\frac{d}{d x} (x^{2} - 4 x y + y^{2}) = 4

y = 2 x + 3 x^{2} + 4 x + c_{1}, y = 2 x - 3 x^{2} + 4 x + c_{1}

Solution steps

\frac{d}{d x} (x^{2} - 4 x y + y^{2}) = 4

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

then

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

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

\int 4 d x = 4 x + c_{1}

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

Isolate

y : y = 2 x + 3 x^{2} + 4 x + c_{1}, y = 2 x - 3 x^{2} + 4 x + c_{1}

y = 2 x + 3 x^{2} + 4 x + c_{1}, y = 2 x - 3 x^{2} + 4 x + c_{1}

\int \frac{3 + z}{1 - z ^{2}} d z

n = 0 \sum \infty \frac{1}{n ^{2}} x^{n}

y = \frac{2}{3} x^{\frac{3}{2}} + 3, [0, 2]

y = x^{n}

\frac{6}{y} d x = (e^{3 x} + 1) d y

What is the solution for derivative of x^2-4xy+y^2=4 ?
The solution for derivative of x^2-4xy+y^2=4 is y=2x+sqrt(3x^2+4x+c_{1)},y=2x-sqrt(3x^2+4x+c_{1)}