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:
1.5
Step-by-step explanation:
12 / 8 = 1.5
My guess would be less than $25
Answer:
on question #2, the answer is A.
Step-by-step explanation:
19-5 is 14.
<em>Hope this helps!</em>
Answer: The answer is 252
Step-by-step explanation:
:)))