What is the solution for dx+e^{8x}dy=0 ?

The solution for dx+e^{8x}dy=0 is y= 1/8 e^{-8x}+c_{1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

dx+e^{8x}dy=0

d x + e^{8 x} d y = 0

y = \frac{1}{8} e^{- 8 x} + c_{1}

Solution steps

d x + e^{8 x} d y = 0

Let

y

be the dependent variable. Divide by

d x

1 + e^{8 x} \frac{d y}{d x} = 0

Substitute

\frac{d y}{d x}

with

y^{'} (x)

1 + e^{8 x} y^{^{'}} (x) = 0

Isolate

y^{'} (x) : y^{'} (x) = - \frac{1}{e ^{8 x}}

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

then

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

y = \int - \frac{1}{e ^{8 x}} d x

\int - \frac{1}{e ^{8 x}} d x = \frac{1}{8} e^{- 8 x} + c_{1}

y = \frac{1}{8} e^{- 8 x} + c_{1}

\frac{\partial}{\partial v} (sin (v) cos (u))

\int \frac{sin ( 2 x )}{28 + cos ^{2} ( x )} d x

y^{^{'}} - y = 1

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{- x} \cdot sin (x)

What is the solution for dx+e^{8x}dy=0 ?
The solution for dx+e^{8x}dy=0 is y= 1/8 e^{-8x}+c_{1}