en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^4+1)y=0

Solution

(d^{4} + 1) 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

(d^{4} + 1) 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^{''''}+9y^{''}=0

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

25y^{''}-120y^'+144y=0

25 y^{^{''}} - 120 y^{^{'}} + 144 y = 0

y^{'''}-7y^{''}+16y^'-12y=0

y^{^{'''}} - 7 y^{^{''}} + 16 y^{^{'}} - 12 y = 0

2y^{''}+4y^'+4y=0

2 y^{^{''}} + 4 y^{^{'}} + 4 y = 0

y^{''}-4y^'+y=0,y(0)=3,y^'(0)=5

y^{^{''}} - 4 y^{^{'}} + y = 0, y (0) = 3, y^{^{'}} (0) = 5

Frequently Asked Questions (FAQ)

What is the solution for (d^4+1)y=0 ?
The solution for (d^4+1)y=0 is