What is implicit e^{x/y}=5x-y ?

The answer to implicit e^{x/y}=5x-y is (dy)/(dx)=(5y^2-e^{x/y}y)/(-e^{x/y)x+y^2}

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implicit e^{x/y}=5x-y

implicit derivative

e^{\frac{x}{y}} = 5 x - y

\frac{d y}{d x} = \frac{5 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

Solution steps

e^{\frac{x}{y}} = 5 x - y

Treat

y

y (x)

Differentiate both sides:

\frac{e ^{\frac{x}{y}} ( y - x \frac{d y}{d x} )}{y ^{2}} = 5 - \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{5 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

\frac{d y}{d x} = \frac{5 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

(t - 2)^{2}

\int_{1}^{4} \frac{x ^{2} + 8}{5 x - x ^{2}} d x

\int \frac{3. 2 ^{x} - 2. 3 ^{x}}{2 ^{x}} d x

\int \frac{42 x}{3 x ^{2} + e} d x

y^{^{'}} + y + 2 sin (x) = 0

What is implicit e^{x/y}=5x-y ?
The answer to implicit e^{x/y}=5x-y is (dy)/(dx)=(5y^2-e^{x/y}y)/(-e^{x/y)x+y^2}