What is the solution for (dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3) ?

The solution for (dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3) is y=(ln(x^2-6x+18))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3)

\frac{d y}{d x} = (x - 3) e^{- 2 y}, y (3) = ln (3)

y = \frac{ln ( x ^{2} - 6 x + 18 )}{2}

Solution steps

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

Solve separable ODE:

y = \frac{ln ( x ^{2} - 6 x + 18 )}{2}

y = \frac{ln ( x ^{2} - 6 x + 18 )}{2}

y = lo g_{2} (lo g_{2} (x))

x \to 1 lim (- \frac{x ^{2}}{2} + 2 x + 4)

\frac{d}{d x} (\frac{x ^{3}}{3} - 10 x^{2} + 100 x)

(1 - x y) d x + (x y - x^{2}) d y = 0

\int tan^{2} (x) x d x

What is the solution for (dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3) ?
The solution for (dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3) is y=(ln(x^2-6x+18))/2