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irinina [24]
3 years ago
8

6xy (1/2x ^2 - 1/2xy + 1/2y ^2 )

Mathematics
1 answer:
nevsk [136]3 years ago
6 0
Is this correct on what you typed above -> \bf 6xy\left( \cfrac{1}{2x^2}-\cfrac{1}{2xy}+\cfrac{1}{2y^2} \right) ?
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Please help me with the below question.
VMariaS [17]

By letting

y = \displaystyle \sum_{n=0}^\infty c_n x^{n+r}

we get derivatives

y' = \displaystyle \sum_{n=0}^\infty (n+r) c_n x^{n+r-1}

y'' = \displaystyle \sum_{n=0}^\infty (n+r) (n+r-1) c_n x^{n+r-2}

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

5r(r-1) c_0 x^{r-1} + \displaystyle \sum_{n=1}^\infty \bigg( (n+r+1) c_n + (n + r + 1) (5n + 5r + 1) c_{n+1} \bigg) x^{n+r} = 0

Examine the lowest degree term \left(x^{r-1}\right), which gives rise to the indicial equation,

5r (r - 1) + r = 0 \implies 5r^2 - 4r = r (5r - 4) = 0

with roots at r = 0 and r = 4/5.

b) The recurrence for the coefficients c_k is

(k+r+1) c_k + (k + r + 1) (5k + 5r + 1) c_{k+1} = 0 \implies c_{k+1} = -\dfrac{c_k}{5k+5r+1}

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

c_{k+1} = -\dfrac{c_k}{5k+5} \implies \boxed{g(k) = -\dfrac1{5k+5}}

c) Starting with c_0=1, we find

c_1 = -\dfrac{c_0}5 = -\dfrac15

c_2 = -\dfrac{c_1}{10} = \dfrac1{50}

so that the first three terms of the solution are

\displaystyle \sum_{n=0}^2 c_n x^{n + 4/5} = \boxed{x^{4/5} - \dfrac15 x^{9/5} + \frac1{50} x^{13/5}}

4 0
2 years ago
What is the value of c in the equation below? StartFraction 5 Superscript 5 Baseline Over 5 squared EndFraction = a Superscript
maw [93]

Answer:

125

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help me with this!
mafiozo [28]
A (-5, 6)
B (-5, 2)
C (-9, 2)
D (-9, 6)

As it is just a rotation around the origin by 180, you can just change the sign in front of the numbers :)
4 0
3 years ago
A fence is being built around the local park in order to ensure the safety of children as they play. The rectangular park is 15
vladimir2022 [97]

Answer:

1. perimeter

2. 50

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Remainders and leftlover. Is the same?
horrorfan [7]
Yes. They both mean the same thing.
8 0
3 years ago
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