(d^3+1)y=cos(2x-1)

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Solution for (d^3+1)y=cos(2x-1) equation: 


Simplifying
(d3 + 1) * y = cos(2x + -1)

Reorder the terms:
(1 + d3) * y = cos(2x + -1)

Reorder the terms for easier multiplication:
y(1 + d3) = cos(2x + -1)
(1 * y + d3 * y) = cos(2x + -1)

Reorder the terms:
(d3y + 1y) = cos(2x + -1)
(d3y + 1y) = cos(2x + -1)

Reorder the terms:
d3y + 1y = cos(-1 + 2x)
d3y + 1y = (-1 * cos + 2x * cos)
d3y + 1y = (-1cos + 2cosx)

Solving
d3y + 1y = -1cos + 2cosx

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-1y' to each side of the equation.
d3y + 1y + -1y = -1cos + 2cosx + -1y

Combine like terms: 1y + -1y = 0
d3y + 0 = -1cos + 2cosx + -1y
d3y = -1cos + 2cosx + -1y

Divide each side by 'y'.
d3 = -1cosy-1 + 2cosxy-1 + -1

Simplifying
d3 = -1cosy-1 + 2cosxy-1 + -1

Reorder the terms:
d3 = -1 + 2cosxy-1 + -1cosy-1

Reorder the terms:
1 + -2cosxy-1 + cosy-1 + d3 = -1 + 2cosxy-1 + -1cosy-1 + 1 + -2cosxy-1 + cosy-1

Reorder the terms:
1 + -2cosxy-1 + cosy-1 + d3 = -1 + 1 + 2cosxy-1 + -2cosxy-1 + -1cosy-1 + cosy-1

Combine like terms: -1 + 1 = 0
1 + -2cosxy-1 + cosy-1 + d3 = 0 + 2cosxy-1 + -2cosxy-1 + -1cosy-1 + cosy-1
1 + -2cosxy-1 + cosy-1 + d3 = 2cosxy-1 + -2cosxy-1 + -1cosy-1 + cosy-1

Combine like terms: 2cosxy-1 + -2cosxy-1 = 0
1 + -2cosxy-1 + cosy-1 + d3 = 0 + -1cosy-1 + cosy-1
1 + -2cosxy-1 + cosy-1 + d3 = -1cosy-1 + cosy-1

Combine like terms: -1cosy-1 + cosy-1 = 0
1 + -2cosxy-1 + cosy-1 + d3 = 0

The solution to this equation could not be determined.

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