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

The solution for (dy)/(dx)=(x-5)e^{-2y},y(5)=ln(5) is y=(ln(x^2-10x+50))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = \frac{ln ( x ^{2} - 10 x + 50 )}{2}

Solution steps

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

Solve separable ODE:

y = \frac{ln ( x ^{2} - 10 x + 50 )}{2}

y = \frac{ln ( x ^{2} - 10 x + 50 )}{2}

\int \frac{3 x ^{2}}{49 - x ^{2}} d x

\int \frac{e ^{y}}{( e ^{y} + 1 ) ^{2}} d y

y^{^{'}} = \frac{y \cdot e ^{x}}{x}

\int_{3}^{4} \frac{x}{x ^{2} + 4 x + 20} d x

\frac{d}{d x} ((4 x^{2} - 2 x)^{4})

What is the solution for (dy)/(dx)=(x-5)e^{-2y},y(5)=ln(5) ?
The solution for (dy)/(dx)=(x-5)e^{-2y},y(5)=ln(5) is y=(ln(x^2-10x+50))/2