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

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

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dx+dye^{6x}=0

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

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

Solution steps

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

Let

y

be the dependent variable. Divide by

d x

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

Substitute

\frac{d y}{d x}

with

y^{'} (x)

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

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