Add 3x to both sides
-3x+10=3x-8
+3x +3x
10=6x-8
+ 8 +8
18=6x
/ / (divide)
6. 6
3=x
We want a solution in the form
with derivatives
Substituting and its derivatives into the ODE,
gives
Shift the index on the second sum to have it start at :
and take the first term out of the other two sums. Then we can consolidate the sums into one that starts at :
and so the coefficients in the series solution are given by the recurrence,
or more simply, for ,
Note the dependency between every other coefficient. Consider the two cases,
- If , where is an integer, then
and so on, with the general pattern
- If , then
and we would see that for all .
So we have
so that one solution is
and the other is
I've attached a plot of the exact and series solutions below with , , and to demonstrate that the series solution converges to the exact one.
Answer: 50.77
It says I need more characters, so I’m adding this
Answer:
Its H or J
I Would go with J tho...
<u>not all the way sure</u>
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