What is the solution for dx+e^{6x}dy=0 ?

The solution for dx+e^{6x}dy=0 is y= 1/6 e^{-6x}+c_{1}

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dx+e^{6x}dy=0

d x + e^{6 x} d y = 0

y = \frac{1}{6} e^{- 6 x} + c_{1}

Solution steps

d x + e^{6 x} d y = 0

Let

y

be the dependent variable. Divide by

d x

1 + e^{6 x} \frac{d y}{d x} = 0

Substitute

\frac{d y}{d x}

with

y^{'} (x)

1 + e^{6 x} y^{^{'}} (x) = 0

Isolate

y^{'} (x) : y^{'} (x) = - \frac{1}{e ^{6 x}}

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

then

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

y = \int - \frac{1}{e ^{6 x}} d x

\int - \frac{1}{e ^{6 x}} d x = \frac{1}{6} e^{- 6 x} + c_{1}

y = \frac{1}{6} e^{- 6 x} + c_{1}

x y^{^{'}} - y = x^{2} cos (x)

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2 (x^{3} - x)^{4}

n = 2 \sum \infty \frac{2}{n ^{3}}

What is the solution for dx+e^{6x}dy=0 ?
The solution for dx+e^{6x}dy=0 is y= 1/6 e^{-6x}+c_{1}