What is implicit x^2+xy-y^2=4 ?

The answer to implicit x^2+xy-y^2=4 is (dy)/(dx)=(-2x-y)/(x-2y)

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implicit x^2+xy-y^2=4

implicit derivative

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

\frac{d y}{d x} = \frac{- 2 x - y}{x - 2 y}

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

2 x + y + x \frac{d y}{d x} - 2 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 2 x - y}{x - 2 y}

\frac{d y}{d x} = \frac{- 2 x - y}{x - 2 y}

16 y^{^{''}} + 72 y^{^{'}} + 87 y = 0, y (0) = 2, y^{^{'}} (0) = 4

\frac{d v}{d x} - 8 v = 10

\frac{d y}{d x} (3) + (x y + 5 x) = 0

\int \frac{( ln ( x ) ) ^{18}}{x} d x

\int 4 x e^{2 x} d x

What is implicit x^2+xy-y^2=4 ?
The answer to implicit x^2+xy-y^2=4 is (dy)/(dx)=(-2x-y)/(x-2y)