What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+7y=0 ?

The solution for (d^2y)/(dx^2)+4(dy)/(dx)+7y=0 is y=e^{-2x}(c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x))

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)+7y=0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 7 y = 0

y = e^{- 2 x} (c_{1} cos (3 x) + c_{2} sin (3 x))

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 7 y = 0

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (3 x) + c_{2} sin (3 x))

y = e^{- 2 x} (c_{1} cos (3 x) + c_{2} sin (3 x))

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} - 15 y = 0

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

y^{^{''}} - 4 y - 4 y = 0

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

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

What is the solution for (d^2y)/(dx^2)+4(dy)/(dx)+7y=0 ?
The solution for (d^2y)/(dx^2)+4(dy)/(dx)+7y=0 is y=e^{-2x}(c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x))