en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

(d^6-1)y=0

Solution

(d^{6} - 1) y = 0

Solution

y = c_{1} e^{x} + c_{2} e^{- x} + e^{\frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + e^{- \frac{x}{2}} (c_{5} cos (\frac{3 x}{2}) + c_{6} sin (\frac{3 x}{2}))

Solution steps

(d^{6} - 1) y = 0

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + e^{\frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + e^{- \frac{x}{2}} (c_{5} cos (\frac{3 x}{2}) + c_{6} sin (\frac{3 x}{2}))

y = c_{1} e^{x} + c_{2} e^{- x} + e^{\frac{x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2})) + e^{- \frac{x}{2}} (c_{5} cos (\frac{3 x}{2}) + c_{6} sin (\frac{3 x}{2}))

Graph

Popular Examples

y^{''}+16y=0,y(0)=0,y(1)=1

12y^{''}+64y=0,y(0)=4,y^'(0)=7

y^{''}-8y^'+25y=0,y(0)=e^{4x}cos(3x)

81y^{''''}=256y

linear (d^2y)/(dx^2)=16y

Frequently Asked Questions (FAQ)

What is the solution for (d^6-1)y=0 ?
The solution for (d^6-1)y=0 is