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


<u>Answer:</u>
D) 6x^2 - 8y^2 = 50
-6x^2 - 2y^2 = 11
<u>Step-by-step explanation:</u>
We are given the following two expressions:

and

Now if we look at the option D)
and
, we can observe that the earlier part in the given expression is just a simplification of 6x^2 - 8y^2 = 50.

and the later part
is already the same.
Therefore, the correct answer option is D) 6x^2 - 8y^2 = 50
-6x^2 - 2y^2 = 11.
Answer:
x= 11
A=59
B= 37
C = 84
Step-by-step explanation:
A triangle adds up to 180 °.
So the equation will be a °+ b° + c° = 180°
Next, you combine like terms.

Then inverse operation,

After to get a, b, and c you just need to plug in x.

Answer:
the numbers next to a variable is a coefficient, for instance in 2x 2 would be the coefficient.
the constants are the numbers without variables next to them, just numbers
like terms are the term that are similar like 2x and 8x or even 5 and 3
lm not exactly sure what they mean when asking for constant terms.