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jeyben [28]
3 years ago
11

In this exercise, we consider finding the first five coefficients in the series solution of the first-order linear initial value

problem (x²+2)y′′ − 6y = 0 subject to the initial condition y(0) = 1, y′(0) = 2. Since the equation has an ordinary point at x=0 and it has a power series solution in the form y = Lim(n=0→[infinity])Σ cₙxⁿ.(1) Insert the formal power series into the differential equation and derive the recurrence relation: cn= __________cₙ₋₂ for n=2,3,⋯ The solution to this initial value problem can be written in the form y(x)= c₀y₁(x)+c₁y₂(x) where c₀ and c₁ are determined from the initial conditions. The function y₁(x) is an even function and y₂(x) is an odd function. For this example, from the initial conditions, we have c₀ = ______ and c₁ = ______. The function y₁(x) is an infinite series y₁(x) = 1+ Lim(n=1→[infinity])Σ aₙx²ⁿNote that the constant c₀ has been factored out. (2) Use the recurrence relation to find the first few coefficients of the infinite series: a₂ = _______, a₄ = _______, a₆ = _______, a₈ = _______.Note that the constant c₀ has been factored out. Finally the polynomial y₂(x)= _______NOTE: The function y₂(x) is an odd degree polynomial with first term x. In other words, note that the constant c₁ has been factored out.

Mathematics
1 answer:
Ghella [55]3 years ago
7 0

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images for the step by step explanation for the answer to the question

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PLZ HELP ME ASAP PLZ PLZ PLZ!!!!! I NEED LOTS OF HELP!!! I USED 40 POINTS
cupoosta [38]
First, some defintions
reciprocals are like a/b and b/a or 5/1 and 1/5

remember, \frac{\frac{a}{b}}{\frac{c}{d}}=(\frac{a}{b})(\frac{d}{c})=\frac{ad}{bc}

john's fraction is reciprocal of sarah's
john=a/b
sarah=b/a

david multiplies his by sarah and gets 12/35
(b/a)(david)=12/35

multplies his number by john and gets 12/35
(a/b)(david)=15/7

hmmm

(b/a)(david)=12/35 and
(a/b)(david)=15/7

if we divide them then we do
\frac{(\frac{b}{a})(david)}{(\frac{a}{b})(david)}=\frac{\frac{12}{35}}{\frac{15}{7}}=
\frac{\frac{b}{a}}{\frac{a}{b}}=\frac{\frac{12}{35}}{\frac{15}{7}}=
(\frac{b}{a})(\frac{b}{a})=(\frac{12}{35})(\frac{7}{15})=
\frac{b^2}{a^2}=\frac{84}{525}=
\frac{b^2}{a^2}=\frac{4}{25}
square root both sides
\frac{b}{a}=\frac{2}{5}

therefor
b=2 and a=5

john's number is a/b=5/2
sarah's number is 2/5

david, hmm

sarah times david=12/35
2/5 times david=12/35
times both sides by 5/2
david=60/70
david=6/7

check other

john times david=15/7
5/2 times 6/7=15/7
30/14=15/7
15/7=15/7
true





sarah's favorite number is 2/5
john's favorite number is 5/2
david's favorite number is 6/7
6 0
3 years ago
Can someone pls help thanks
kolezko [41]
I think I think that it is 8 hours. Hopefully that helps!
5 0
3 years ago
LaPeach Elementary School uses 4000 pencils each year. The school has 500 students. What is the unit rate per student?
mezya [45]

Answer:

8

Step-by-step explanation:

Unit per student = 4000/500 = 8

6 0
3 years ago
Read 2 more answers
What is half of seven in a whole number
Nikitich [7]
0.7 / 100 = 0.007 or 0.007 x 100 = 0.7 hope this helps

6 0
3 years ago
Alex owns a miniature model of a train. The actual train is 14 feet tall and 70 feet long. If Alex's model is 6 inches tall, wha
rjkz [21]

6 is multiplied by 2 1/3 to get to 14. 70 divided by 2 1/3 is 30. The model of the train is 30 inches long.

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