What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+5y=2e^{-2x} ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)+5y=2e^{-2x} is y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2e^{-2x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)+4(dy)/(dx)+5y=2e^{-2x}

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 2 e^{- 2 x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 2 e^{- 2 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 2 e^{- 2 x}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 2 e^{- 2 x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 2 e^{- 2 x}

\frac{d y}{d t} = 4 y + y^{4}, y (0) = 1

\frac{d}{d x} (\frac{- 24}{x ^{4}})

\int 2 + y e^{y} d y

x \to 0 - lim (\frac{x}{sin ( 3 x )})

\int_{- 4}^{4} x 16 - x^{2} d x

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+5y=2e^{-2x} ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)+5y=2e^{-2x} is y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2e^{-2x}