What are the solutions to the equation y^{(6)}+y=0 ?

The solutions to the equation y^{(6)}+y=0 are y=0,y=-1

Find the zeros of y^{(6)}+y=0

The zeros of y^{(6)}+y=0 are y=0,y=-1

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y^{(6)} + y = 0

y = 0, y = - 1

Solution steps

y^{(6)} + y = 0

Factor

y^{6} + y : y (y + 1) (y^{4} - y^{3} + y^{2} - y + 1)

y (y + 1) (y^{4} - y^{3} + y^{2} - y + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or y + 1 = 0 or y^{4} - y^{3} + y^{2} - y + 1 = 0

Solve

y + 1 = 0 : y = - 1

Solve

y^{4} - y^{3} + y^{2} - y + 1 = 0 :

No Solution for

y \in R

The solutions are

y = 0, y = - 1

x^{3} - 11 = 0

s^{3} + s^{2} + 1

m (m - 1) (m - 2) - 6 = 0

7 x^{6} = - 15

x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 3 = 0

What are the solutions to the equation y^{(6)}+y=0 ?
The solutions to the equation y^{(6)}+y=0 are y=0,y=-1
Find the zeros of y^{(6)}+y=0
The zeros of y^{(6)}+y=0 are y=0,y=-1