What is the solution for (d^3y)/(dx^3)-3(dy)/(dx)-2y=0 ?

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

\frac{d ^{3} y}{d x ^{3}} - 3 \frac{d y}{d x} - 2 y = 0

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x}

Solution steps

\frac{d ^{3} y}{d x ^{3}} - 3 \frac{d y}{d x} - 2 y = 0

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x}

y = c_{1} e^{2 x} + c_{2} e^{- x} + c_{3} x e^{- x}

9 y^{^{''}} + 4 y^{^{'}} + 5 y = 0

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

y^{^{''''}} = y

y^{^{'''}} - 5 y^{^{''}} + 4 y^{^{'}} = 0

y = y^{^{''}}

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