What is the solution for (d^2y)/(dx^2)+10(dy)/(dx)+61y=0 ?

The solution for (d^2y)/(dx^2)+10(dy)/(dx)+61y=0 is y=e^{-5x}(c_{1}cos(6x)+c_{2}sin(6x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)+10(dy)/(dx)+61y=0

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 61 y = 0

y = e^{- 5 x} (c_{1} cos (6 x) + c_{2} sin (6 x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 61 y = 0

Solve linear ODE:

y = e^{- 5 x} (c_{1} cos (6 x) + c_{2} sin (6 x))

y = e^{- 5 x} (c_{1} cos (6 x) + c_{2} sin (6 x))

77 y^{^{''''}} + 219 y^{^{''}} + 100 y = 0

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + 3 y = 4 y^{^{'}}

y^{^{'''}} + 5 y^{^{''}} - 34 y^{^{'}} - 80 y = 0

y^{^{''}} + 1 y = 0, y (\frac{π}{2}) = 3, y^{^{'}} (\frac{π}{2}) = - 1

What is the solution for (d^2y)/(dx^2)+10(dy)/(dx)+61y=0 ?
The solution for (d^2y)/(dx^2)+10(dy)/(dx)+61y=0 is y=e^{-5x}(c_{1}cos(6x)+c_{2}sin(6x))