The next step is to solve the recurrence, but let's back up a bit. You should have found that the ODE in terms of the power series expansion for


which indeed gives the recurrence you found,

but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that

, and substituting this into the recurrence, you find that

for all

.
Next, the linear term tells you that

, or

.
Now, if

is the first term in the sequence, then by the recurrence you have



and so on, such that

for all

.
Finally, the quadratic term gives

, or

. Then by the recurrence,




and so on, such that

for all

.
Now, the solution was proposed to be

so the general solution would be


Answer:
6787.8
explanation:
740.16 + 3047.16 + 2149.76 + 850.72 = 6787.8
i dont actually know if this is it so sorry if not
C^2+7 would equal 88. the first equation states that C=9, so you can just plug in 9 for C
4 ^ (1/7 ) is the 7th root of 4 or the 3rd box
4 ^ (7/2) is 4 to the 7th power then the square root or the 2nd box
7 ^ (1/4) is the 4th root of 7 or the 4th box
7 ^ (1/2) is the square root of 7 or the 6th box