Let

Differentiating twice gives


When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.
Substitute these into the given differential equation:


Then the coefficients in the power series solution are governed by the recurrence relation,

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.
• If n is even, then n = 2k for some integer k ≥ 0. Then




It should be easy enough to see that

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then




so that

So, the overall series solution is


Answer:
the burgers be 3 and fries be 2
Step-by-step explanation:
The computation is shown below:
Let us assume burgers be x
And, the fries be y
Now according to the questiojn
1.25x + 0.50y = $4.75
1.50x + 0.99y = $6.48
Now multiply by 1.2 in the first equation
1.50x + 0.6y = $5.70
1.50x + 0.99y = $6.48
-0.39y = -0.78
y = 2
Now put the value of y in any of the above equation
1.25x + 0.50(2) = $4.75
x = 3
Hence, the burgers be 3 and fries be 2
To find the answer,we can solve this by settin up an equation.
Let x be the number of adult tickets sold.
The number of students ticket sold would be:
x-74
We can then sum them up to set an equation:
x+x-74 = 676
2x = 676 + 74
x = 375
Therefore the adult tickets sold were 375.
Hope it helps!
M(x) = 5x + 4 n(x) = 6x - 9
Part 1 (m + n)(x) = 5x + 4 + 6x - 9
= 11x - 5
Part 2 (m * n)(x) = (5x + 4)(6x - 9) = 30x^2 - 21x - 36
Part 3 m[n(x)] = 5(6x - 9) + 4
= 30x - 45 + 4
= 30x - 41