What is the solution for (dy)/(dx)=(x-2)e^{-2y},y(2)=ln(2) ?

The solution for (dy)/(dx)=(x-2)e^{-2y},y(2)=ln(2) is y=(ln(x^2-4x+8))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=(x-2)e^{-2y},y(2)=ln(2)

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

y = \frac{ln ( x ^{2} - 4 x + 8 )}{2}

Solution steps

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

Solve separable ODE:

y = \frac{ln ( x ^{2} - 4 x + 8 )}{2}

y = \frac{ln ( x ^{2} - 4 x + 8 )}{2}

\int_{0}^{\frac{π}{3}} sin (3 x) d x

\int_{- 4}^{4} 90 d t

x \to 0 lim (\frac{5}{x ^{8}})

\frac{\partial}{\partial x} (e^{3 x} cos (6 y))

\frac{d x}{d t} = 2 + \frac{x}{20}

What is the solution for (dy)/(dx)=(x-2)e^{-2y},y(2)=ln(2) ?
The solution for (dy)/(dx)=(x-2)e^{-2y},y(2)=ln(2) is y=(ln(x^2-4x+8))/2