en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

(d^4y)/(dx^4)+y=0

Solution

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

Solution

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2}))

Solution steps

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

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2}))

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2}) + c_{2} sin (\frac{x}{2})) + e^{- \frac{x}{2}} (c_{3} cos (\frac{x}{2}) + c_{4} sin (\frac{x}{2}))

Graph

Popular Examples

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

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

4(d^2y)/(dx^2)+64y=0

(d^2y)/(dx^2)+k^2y=0

Frequently Asked Questions (FAQ)

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