Answer:
g(t) = 0
And
The differential equation 
is linear and homogeneous
Step-by-step explanation:
Given that,
The differential equation is -
![e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0](https://tex.z-dn.net/?f=e%5E%7Bt%7Dy%27%20%2B%20%289t%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Ce%5E%7Bt%7Dy%27%20%2B%20%28%5Cfrac%7B9t%28t%5E%7B2%7D%20%2B%2081%20%29%20-%201%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Ce%5E%7Bt%7Dy%27%20%2B%20%28%5Cfrac%7B9t%5E%7B3%7D%20%2B%20729t%20%20-%201%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Cy%27%20%2B%20%5B%5Cfrac%7B9t%5E%7B3%7D%20%2B%20729t%20%20-%201%7D%7Be%5E%7Bt%7D%28t%5E%7B2%7D%20%2B%2081%29%20%7D%20%5Dy%20%3D%200)
By comparing with y′+p(t)y=g(t), we get
g(t) = 0
And
The differential equation is linear and homogeneous.
Answer
x-19=27
Step-by-step explanation:
Answer:
-3x + y = -14
Step-by-step explanation:
m = 3/1 = 3
1 = 15 + b
b = -14
Y = 3x - 14
-3x + y = -14
Answer:
x = -2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
8x + 4(x - 3) = 4(6x + ) -4
8x +(4)(x) + (4)(-3) = (4)(6x) + (4)(4) + -4 (distribute)
8x + 4x + -12 = 24x + 16 + -4
(8x) + (4x) +(-12) = (24x) + (16 + -4) (combine like terms)
12x + -12 = 24x + 12
12x -12 = 24x + 12
Step 2: Subtract 24x from both sides.
12x -12 -24x = 24x + 12 -24x
-12x -12 = 12
Step 3: Add 12 to both sides.
-12x - 12 + 12 = 12 + 12
-12x = 24
Step 4: Divide both sides by -12.
-12x/-12 = 24/-12 <u>x = -2</u>
HOPE THIS HELPED!!!
