What is the solution for (d^2y)/(dx^2)+10(dy)/(dx)+41y=0 ?

The solution for (d^2y)/(dx^2)+10(dy)/(dx)+41y=0 is y=e^{-5x}(c_{1}cos(4x)+c_{2}sin(4x))

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)+41y=0

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 41 y = 0

y = e^{- 5 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 41 y = 0

Solve linear ODE:

y = e^{- 5 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

y = e^{- 5 x} (c_{1} cos (4 x) + c_{2} sin (4 x))

x^{^{''}} + x^{^{'}} - x = 0

\frac{d ^{3} y}{d x ^{3}} - y = 0

y^{^{''}} - 3 y^{^{'}} + y 3 = 0

5 y^{^{''}} + 10 y^{^{'}} + 5 y = 0, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 4

What is the solution for (d^2y)/(dx^2)+10(dy)/(dx)+41y=0 ?
The solution for (d^2y)/(dx^2)+10(dy)/(dx)+41y=0 is y=e^{-5x}(c_{1}cos(4x)+c_{2}sin(4x))