What is the solution for (dy)/(dx)=(cos(8x))/(e^{8y)},y(0)=1 ?

The solution for (dy)/(dx)=(cos(8x))/(e^{8y)},y(0)=1 is y=(ln(sin(8x)+e^8))/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=(cos(8x))/(e^{8y)},y(0)=1

\frac{d y}{d x} = \frac{cos ( 8 x )}{e ^{8 y}}, y (0) = 1

y = \frac{ln ( sin ( 8 x ) + e ^{8} )}{8}

Solution steps

\frac{d y}{d x} = \frac{cos ( 8 x )}{e ^{8 y}}

Solve separable ODE:

y = \frac{ln ( sin ( 8 x ) + e ^{8} )}{8}

y = \frac{ln ( sin ( 8 x ) + e ^{8} )}{8}

f (x) = x, at x = 49

\frac{e ^{x}}{x}

\frac{d y}{d x} = 1 + \frac{2}{( y - x ) e ^{3 (y - x)}}

x \to 1 lim (ln (3) + e^{x})

\frac{d}{d x} (ln (4 x - 2 y + 6))

What is the solution for (dy)/(dx)=(cos(8x))/(e^{8y)},y(0)=1 ?
The solution for (dy)/(dx)=(cos(8x))/(e^{8y)},y(0)=1 is y=(ln(sin(8x)+e^8))/8