y(n)+y(n-1)+0.5y(n-2)=x(n)-x(n-1)

Simple and best practice solution for y(n)+y(n-1)+0.5y(n-2)=x(n)-x(n-1) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for y(n)+y(n-1)+0.5y(n-2)=x(n)-x(n-1) equation: 


Simplifying
y(n) + y(n + -1) + 0.5y(n + -2) = x(n) + -1x(n + -1)

Multiply y * n
ny + y(n + -1) + 0.5y(n + -2) = x(n) + -1x(n + -1)

Reorder the terms:
ny + y(-1 + n) + 0.5y(n + -2) = x(n) + -1x(n + -1)
ny + (-1 * y + n * y) + 0.5y(n + -2) = x(n) + -1x(n + -1)

Reorder the terms:
ny + (ny + -1y) + 0.5y(n + -2) = x(n) + -1x(n + -1)
ny + (ny + -1y) + 0.5y(n + -2) = x(n) + -1x(n + -1)

Reorder the terms:
ny + ny + -1y + 0.5y(-2 + n) = x(n) + -1x(n + -1)
ny + ny + -1y + (-2 * 0.5y + n * 0.5y) = x(n) + -1x(n + -1)

Reorder the terms:
ny + ny + -1y + (0.5ny + -1y) = x(n) + -1x(n + -1)
ny + ny + -1y + (0.5ny + -1y) = x(n) + -1x(n + -1)

Reorder the terms:
ny + ny + 0.5ny + -1y + -1y = x(n) + -1x(n + -1)

Combine like terms: ny + ny = 2ny
2ny + 0.5ny + -1y + -1y = x(n) + -1x(n + -1)

Combine like terms: 2ny + 0.5ny = 2.5ny
2.5ny + -1y + -1y = x(n) + -1x(n + -1)

Combine like terms: -1y + -1y = -2y
2.5ny + -2y = x(n) + -1x(n + -1)

Multiply x * n
2.5ny + -2y = nx + -1x(n + -1)

Reorder the terms:
2.5ny + -2y = nx + -1x(-1 + n)
2.5ny + -2y = nx + (-1 * -1x + n * -1x)

Reorder the terms:
2.5ny + -2y = nx + (-1nx + 1x)
2.5ny + -2y = nx + (-1nx + 1x)

Combine like terms: nx + -1nx = 0
2.5ny + -2y = 0 + 1x
2.5ny + -2y = 1x

Solving
2.5ny + -2y = 1x

Solving for variable 'n'.

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

Add '2y' to each side of the equation.
2.5ny + -2y + 2y = 1x + 2y

Combine like terms: -2y + 2y = 0
2.5ny + 0 = 1x + 2y
2.5ny = 1x + 2y

Divide each side by '2.5y'.
n = 0.4xy-1 + 0.8

Simplifying
n = 0.4xy-1 + 0.8

Reorder the terms:
n = 0.8 + 0.4xy-1

See similar equations:

| Y(Y+6)=40 | | 3/4x×3/4x | | 26m^2n-13mn= | | 4/-5*-3/7*2/1 | | -8x-3x-6=12-2x | | x^4-4x^3-11x^2-30x+56=0 | | 28=(2x+1)(x) | | 15=5x/-13 | | 0.15x=141 | | 10=5r/-8 | | x/5-1=(x-4/5) | | (x^2-3)(x^2+x+1)=x^4+x^3-2x^3-3x-3 | | 2=2h/-9 | | 4x^3-19x^2-30x=0 | | 7-2(x+3)=4x-11 | | 3x+1=-3x-4+5x | | 6x+24=96 | | 2=f/-3 | | -10x+0=22 | | -2(2x+3)-4=-2(4x-5) | | 7x-32=5x+8 | | 3(5x-2)=4(x+6) | | -10*0+y=22 | | 5(32-x)=6x-5 | | 5-(x-3)=12-2x | | 5/6(2x-1)-x=x/6 | | -2x+4x+6-6=24-6x | | p^3y+2px=y | | 4x-9/5=3 | | 4x-2x+8=-2(x+5) | | 3(X+7)=2[x-(4-X)] | | 15q= |

Equations solver categories