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

I’m guessing 2 cups or something idk
Slot method
5 slots
1st slot: 20
2nd slot: 19 (1 went to first slot)
3rd slot: 18
4th slot: 17
5th slot: 16
20*19*18*17*16=186,040 ways
You will have to take 3x common from both terms and your ans should look like this,
3x(9x^2-4)