What is the solution for (dy)/(dx)=(x-5)e^{-2y},y(2)=ln(5) ?

The solution for (dy)/(dx)=(x-5)e^{-2y},y(2)=ln(5) is y=(ln(x^2-10x+41))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=(x-5)e^{-2y},y(2)=ln(5)

\frac{d y}{d x} = (x - 5) e^{- 2 y}, y (2) = ln (5)

y = \frac{ln ( x ^{2} - 10 x + 41 )}{2}

Solution steps

\frac{d y}{d x} = (x - 5) e^{- 2 y}

Solve separable ODE:

y = \frac{ln ( x ^{2} - 10 x + 41 )}{2}

y = \frac{ln ( x ^{2} - 10 x + 41 )}{2}

What is the solution for (dy)/(dx)=(x-5)e^{-2y},y(2)=ln(5) ?
The solution for (dy)/(dx)=(x-5)e^{-2y},y(2)=ln(5) is y=(ln(x^2-10x+41))/2