By letting

we get derivatives


a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to

Examine the lowest degree term
, which gives rise to the indicial equation,

with roots at r = 0 and r = 4/5.
b) The recurrence for the coefficients
is

so that with r = 4/5, the coefficients are governed by

c) Starting with
, we find


so that the first three terms of the solution are

Answer:
Note: this answer is kind of long so jump to picture to see a visual process.
In order to find the simplest radical form of a square root, you need prime factorize the number. In order to do this, you take a number and divide it by different prime numbers until all of its factors are now prime. We will use 24 as our example. 24 divided by 2 (which is prime) is 12. 12 divided by 2, is 6. 6 divided by 2 is 3. Therefor, our prime factorization of 24 is 2^3 * 3, which basically means 8 * 3. Then, take take out pairs of the same number and put on the OUTSIDE of the root. However, make sure that it is NEXT to the square root and not inside the mini hook that the square root makes. This means that that number is multiplying the square root of the number. Now, the only pair in this prime factorization is 2, so take two out of the prime factorization and that leaves us with square root 6 times 2, which is the answer.
Also, when taking out pairs, only take one number from the pair (in this case 2) and put it on the outside. If there is another pair, multiply that number by the other number. So if there was a pair of 3 and a pair of 2, take out 1 three and 1 two and multiply them and put on the outside.
Step-by-step explanation:
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Answer:
g(x) = sin(x)
f(x) = e^x
Step-by-step explanation:
Answer:
225
Step-by-step explanation:
360 - 135 = 225