Answer:
The complete solution is
Step-by-step explanation:
Given differential equation is
3y"- 8y' - 3y =4
The trial solution is

Differentiating with respect to x

Again differentiating with respect to x

Putting the value of y, y' and y'' in left side of the differential equation


The auxiliary equation is




The complementary function is

y''= D², y' = D
The given differential equation is
(3D²-8D-3D)y =4
⇒(3D+1)(D-3)y =4
Since the linear operation is
L(D) ≡ (3D+1)(D-3)
For particular integral

[since
]
[ replace D by 0 , since L(0)≠0]

The complete solution is
y= C.F+P.I

Answer:
1.5x = 6
Step-by-step explanation:
This represents 1.5 times the amounts a bucket holds. (I'm assuming you mean x when you typed z)
Answer:
27
Step-by-step explanation:
Lets find the rate of selling:
Let v= the rate of selling, b = number of bottles of water, and t = time:
b over t gives us the
rate of selling:
3 hours is 60min * 3 = 180 mins, and since v=b/t, vt=b:
(0.15) * 180 = 27 bottles of water
(y2-y1)/(x2-x1) (-3 - (-8))/(6- (-5))= 5/11