10. One of the following could be a series solution for y + 5xy + y = 6 In x + 4 where y (1) = -1, y (1) = 1 7(x-1)5 -2 + x – *-1)* + 7r=1)5 20 + ...

Q: what is the generating function of an  an+1=4an-an-1 (n>2)  a0=1, a1=1, a2=4

A: We have been given a recurrence relation . an+1=4an-an-1 , a0=1 , a1=1,a2=4  For , homogenous…

Q: X4 X6 x8 x10 3. Y = x2 + 3! N Terms ** * ... 5! 16 1L +

A: Please rate and feel free to ask any query

Q: (b) Compute the values of each of the following expressions: i. () ii. (1), (1) iii. (2), ), iv. 6).…

A: The expressions are given in the form .It represents the combination of  out of .The formula for…

Q: Find the equation of the elipse

A:

Q: Compute the following: (a) 4!, (b) (), (c) (₂), (d) (), (e) (7), (f) (2)-(2) where n is a…

A:

Q: Find the coefficient B3 in this partial fraction expansion: F(s) a. B₂ 1 b. B₂ = -4 = 16 (s+3)…

A: We have,

Q: 7. Prove that if a, = 1, a1 = 4, and a, = 6a,-1 – 9an-2 for n > 2, then a, = 3"-(3 + n) for all n 2…

A: We have to prove the following result by using the principle of mathematical induction.

Q: For this problem, carry at least four digits after the decimal in your calculations. Answers may…

A: The random variable persons who recaptured follow normal distribution. The number of successes is…

Q: Q2 /Find the solution of the following series x24 + 24 for x-4

A: Given series is                     Y=x22+x44+x66+...+x2424 The compact form of the series is…

Q: 1. A ball is drawn from a 4 blue and 3 red balls it is replaced and ano ocess goes on 16 tim

A: An urn contains 5 white, 4 blue and 3 red balls. Total balls is 5+4+3=12. P(red)=3/12=0.25 Let X be…

Q: 2) By using the iterative formula x+1= and x, 1.5, then the value of x, is O 0.3652 O 1.3652 10 of…

A: Given That :  x2+4x=10 and  xn+1=10xn+1 is the iterative formula for the given equation in [1,2] and…

Q: (a) (b) Use the quotient-remainder theorem to find the gef{77, 42}. Find ALL integer solutions to…

A: Using quotient remainder theorem we can find the gcf is 7 and all integer solution are q=6n+5 and…

Q: Use the table of frequently used Taylor series to find the sum of the series. 8 X-X +X x2 -x5 11 14

A:

Q: b) Given an RL circuit with the equation UTM UTM IP L +RI = 900, dt where L is the inductance, R is…

A: Here we will find out the required value.

Q: n (n + () A k=0 | B, = 0.

A:

Q: The great Swiss mathematician Leonhard Euler sometimes reached incorrect conclusions in his…

A:

Q: Give combinatorial proofs of the following identities. (a) {"} = 2"-1 – 1. (b) {„",} = (3). (c)…

A: Given: Let us show the combinatorial proofs of the following identities a) n2=2n-1-1 b) nn-1=n2 c)…

Q: Suppose you want to type sequences of vowels (that is, the letters a, e, i, o and u). However, the e…

A: Given  the number of sequences of length   (i) Find (ii) Write a second-order difference equation…

Q: Problem 8.1. Show: for all neZ+, we have (1 + 1) + (1 + 3) + (1 + 5) +...+(1+ (2n-1)) = n² + n.

A: The above given mathemtical statement depends on set of natural numbers. Therefore, we can use…

Q: 3. (a) Find a closed formula for the generating function A(z) of the sequence an (3n-7) (-2)".

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 11. One of the following could be a series solution for y + 5xy + y = 6 lnx + 4 where y (1) = –1, y…

A: Taylor series of a function f(x) about x=a is given by:…

Q: 1. Suppose that for a certain life , S×(x) =1- 100 Find (i) Find the prob. that a person aged 25…

A: Given problem is :

Q: 4. One of the following could be a series solution for y-xy = 0 with y(0) = 3, y (0) = 0 O3- 60 90…

A: Here we solve the problem by cross check the option  that is we use option elimination method .

Q: 3. For what value of r does the series 1+r+r² + r³ + • = 10 ?

A:

Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

A:

Q: zu +16n + 20.

A: Given: An expression n2+16n+20 To find All possible remainder when it is divided by 11.As per our…

Q: 1. Suppose that for a certain life , S, (x) = 1- . Find 100 (i) Find the prob. that a person aged 25…

A: Given : The survival function for a certain life is : SXx=1-x1002

Q: Find a power series solution of y" + (1+x²)y=0 13 a. ao(1-x². - + x² + ...) + a₁(x-²1²x³- 24 720 13…

A:

Q: (d) Prove that 2" +3" is a multiple of 5 for all odd n E N.

A: Use the mathematical induction to prove the given statement.

Q: 4. The first four non-zero terms of the Taylor series for cot(x) about x = are 2 4 3 IT cot(x) = 1 −…

A: Step 1:

Q: If n(A) = 9, n(B) = 12, and n(ANB) = 5, what is n(AUB)?

A:

Q: Q3/ Find the solution of the following series x12 + 13 + 7 for x=2

A: Step:-1 Given that Y = x23 + x45 + x67 +.....+ x1213Y= x23 + x225 + x237 +.....+ x2613Y=∑n=16x2n2n+1…

Q: Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we…

A: Decomposing Unit FractionsThe problem of decomposing a unit fraction as the sum of two other unit…

Q: 5. For n ≥ 1, establish the formula (2n + 1)² = (4tn + 1)² – (4tn)².

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.