Polynomial. The difference between a polynomial and - 5Y & # 178; - 13y is - Y & # 178; + 3y-1 2. Given X-Y = 3, xy = 2, find the difference of (3y-2x + 2x + XY) - (- 5x + 6xy + 6y) 3. Given a = 2m & # 178; n-mn & # 178;, A-B = 0, find B

Polynomial. The difference between a polynomial and - 5Y & # 178; - 13y is - Y & # 178; + 3y-1 2. Given X-Y = 3, xy = 2, find the difference of (3y-2x + 2x + XY) - (- 5x + 6xy + 6y) 3. Given a = 2m & # 178; n-mn & # 178;, A-B = 0, find B

The difference between a polynomial and - 5Y & # 178; - 13y is - Y & # 178; + 3y-1,
This polynomial = - Y & # 178; + 3y-1 + (- 5Y & # 178; - 13y)
=-y²+3y-1-5y²-13y
=-6y²-10y-1
2. It is known that X-Y = 3, xy = 2
(y+3)y=2
y^2+3y-2=0
y=(-3+√9+4*1*2)/2=(-3+√17)/2
Or y = (- 3 - √ 9 + 4 * 1 * 2) / 2 = (- 3 - √ 17) / 2
（3y-2x+2x+xy)-（-5x+6xy+6y)
=3y-2x+2x+xy+5x-6xy-6y
=-3y+5x-5xy
=-3y+5(y+3)-5*2
=-3y+5y+15-10
=2y+5
（1）y=(-3+√17)/2
The above formula = 2 * (- 3 + √ 17) / 2 + 5
=2+√17
（2）y=(-3-√17)/2
The above formula = 2 * (- 3 - √ 17) / 2 + 5
=2-√17
3. Given a = 2m & # 178; n-mn & # 178;, A-B = 0, find B
A-B=0
B=A
B=2m²n-mn²

Equations: 3Y = x + 4, 2x + 5Y = - 19, find the value of X and y

3Y = x + 4 multiply both sides by 2 to get 6y = 2x + 8, so 2x = 6y-8
2X + 5Y = - 19 substitute 2x = 6y-8 to get:
6y-8+5y=-19
11y = - 11, so y = - 1
Substituting y = - 1 into 2x = 6y-8, we get the following result:
2x=-6-8
x=-7
So y = - 1, x = - 7

5y''+4y'+3y=e^(-t),y(0)=y'(0)=1

Homogeneous equation 5Y '' + 4Y '+ 3Y = 0
y=e^(-2t/5)*(C1cos22^0.5t/5+C2sin22^0.5t/5)
Nonhomogeneous equation 5Y '' + 4Y '+ 3Y = e ^ (- t)
Special solution y = e ^ (- t) / 5D ^ 2 + 4D + 3 = e ^ (- t) / 4
y=e^(-2t/5)*(C1cos22^0.5t/5+C2sin22^0.5t/5)+e^(-t)/4