(D-2)(xD+1)y=senx

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Solution for (D-2)(xD+1)y=senx equation: 


Simplifying
(D + -2)(xD + 1) * y = senx

Reorder the terms:
(-2 + D)(xD + 1) * y = senx

Reorder the terms:
(-2 + D)(1 + xD) * y = senx

Reorder the terms for easier multiplication:
y(-2 + D)(1 + xD) = senx

Multiply (-2 + D) * (1 + xD)
y(-2(1 + xD) + D(1 + xD)) = senx
y((1 * -2 + xD * -2) + D(1 + xD)) = senx
y((-2 + -2xD) + D(1 + xD)) = senx
y(-2 + -2xD + (1 * D + xD * D)) = senx
y(-2 + -2xD + (1D + xD2)) = senx

Reorder the terms:
y(-2 + 1D + -2xD + xD2) = senx
y(-2 + 1D + -2xD + xD2) = senx
(-2 * y + 1D * y + -2xD * y + xD2 * y) = senx

Reorder the terms:
(-2xyD + xyD2 + -2y + 1yD) = senx
(-2xyD + xyD2 + -2y + 1yD) = senx

Solving
-2xyD + xyD2 + -2y + 1yD = ensx

Solving for variable 'x'.

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

Add '-1ensx' to each side of the equation.
-2xyD + xyD2 + -2y + -1ensx + 1yD = ensx + -1ensx

Reorder the terms:
-1ensx + -2xyD + xyD2 + -2y + 1yD = ensx + -1ensx

Combine like terms: ensx + -1ensx = 0
-1ensx + -2xyD + xyD2 + -2y + 1yD = 0

Add '2y' to each side of the equation.
-1ensx + -2xyD + xyD2 + -2y + 2y + 1yD = 0 + 2y

Combine like terms: -2y + 2y = 0
-1ensx + -2xyD + xyD2 + 0 + 1yD = 0 + 2y
-1ensx + -2xyD + xyD2 + 1yD = 0 + 2y
Remove the zero:
-1ensx + -2xyD + xyD2 + 1yD = 2y

Add '-1yD' to each side of the equation.
-1ensx + -2xyD + xyD2 + 1yD + -1yD = 2y + -1yD

Combine like terms: 1yD + -1yD = 0
-1ensx + -2xyD + xyD2 + 0 = 2y + -1yD
-1ensx + -2xyD + xyD2 = 2y + -1yD

Reorder the terms:
-1ensx + -2xyD + xyD2 + -2y + yD = 2y + -2y + -1yD + yD

Combine like terms: 2y + -2y = 0
-1ensx + -2xyD + xyD2 + -2y + yD = 0 + -1yD + yD
-1ensx + -2xyD + xyD2 + -2y + yD = -1yD + yD

Combine like terms: -1yD + yD = 0
-1ensx + -2xyD + xyD2 + -2y + yD = 0

The solution to this equation could not be determined.

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