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:
2,535,008
two million , five hundred thirty five thousand, eight
Answer:
x = 1/8 = 0.125
Step-by-step explanation: Add 1 to both sides of the equation :
8x = 1
Divide both sides of the equation by 8:
x = 1/8 = 0.125
If 1/6 of the bags of pet food are cat food, then the other 5/6 is other pet food.
Since there are 4 bags that make up 1/6 of the food, multiplying 4 by 6 should get the answer. 4 x 6 = 24