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


Simplifying a fraction means most likely having it remain as a fraction and not a whole number and it can be converted as a decimal.
on the other hand, simplifying a radical, you would have no remainders, fractions, or decimals after simplifying.
thats the difference.
im not sure about similarities
Answer: 66 because you are adding 2 then 4 then 6 then 8 then 10 then 12 therefore 17+10= 27, and 27+12= 39 and 39+27 equals 66
Answer:
first what you do is divide two and then for and then after you divide them together you can get your number so I'm going to show you example how to do it
Step-by-step explanation:
first divide 4 / 2 and then you can get your answer after you divide that
Answer:
D. AC ≅ XZ
Step-by-step explanation:
To prove that two triangles are congruent by the Angle-Side-Angle theorem, both triangles must have two corresponding angles that are congruent to each other in each triangle, and also a corresponding included side in each triangle that are congruent.
Thus, we are given that,
<X ≅ <A and <Z ≅ <C, therefore, what is needed is a corresponding included angle in each triangle that are congruent to each other, which are,
AC and XZ
Therefore, what is needed is:
AC ≅ XZ