What is the solution for (d^3y)/(dx^3)-8y=0 ?

The solution for (d^3y)/(dx^3)-8y=0 is y=c_{1}e^{2x}+e^{-x}(c_{2}cos(sqrt(3)x)+c_{3}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^3y)/(dx^3)-8y=0

\frac{d ^{3} y}{d x ^{3}} - 8 y = 0

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

Solution steps

\frac{d ^{3} y}{d x ^{3}} - 8 y = 0

Solve linear ODE:

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

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

y^{^{''''}} - 24 y^{^{'''}} + 144 y^{^{''}} = 0

(D^{4} - D^{3} - 7 D^{2} + 3 D) y = 0

3 y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = - 6, y^{^{'}} (0) = - 18

y^{^{''}} + 42 y^{^{'}} + 8 y = 0

\frac{d ^{3} y}{d x ^{3}} - 21 \frac{d y}{d x} - 20 y = 0

What is the solution for (d^3y)/(dx^3)-8y=0 ?
The solution for (d^3y)/(dx^3)-8y=0 is y=c_{1}e^{2x}+e^{-x}(c_{2}cos(sqrt(3)x)+c_{3}sin(sqrt(3)x))