(a) Check whether the IVP = y(0) = 4. -4' satisfies the hypotheses of the Picard-Lindelöf theorem. X Y (b) Find all the solutions of the IVP defined in (a). Is this result in contradiction with the result obtained in (a)? Explain your answer.

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A:

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A: To evaluate the following integral.

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A: Let us take f(x)=x3 − x − 1 So, f'(x)= 3x2 - 1 Given x1 = 1

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A:

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A: To verify the given expression is followed by matrix X .

Q: 2:2 + [3] x + 2 = [0] in Z6.

A: The solution given below with attached file.Explanation:

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A:

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A:

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A:

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A:

Q: (a) Use the Intermediate Theorem to prove that Vx + Vx + 7 = 3 has a solution in the interval [0,…

A: We have to use intermediate value theorem.

Q: 6. (x – 1

A:

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A: We have to find the general solution of the differential equation.

Q: Express ƒ(z) = 4x² + i4y² by a formula involving the variables z and ž.

A: Let,

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A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

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A:

Q: Let a +0 be any real number different from 0. If y = f(x) is the solution of y" – ay" = -48+48ax,…

A: the given differential equation is  y'''- a y''= -48 + 48 a x      .....(1) the associated…

Q: 3/(a) Let X × b(n, –) and E(x)= E(16–7x) find n.

A: Solution : Given : X ~ b( n, 14 )             E(x) = E( 16-7x ) To find n : It is known that for…

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A:

Q: 2. (4.4.1 #13) Find a particular solution. y" - 4y + 4y = e²x (1 - 3x + 6x²)

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Q: csc q-2 =0 Find q, 0<q<2p/

A: This question is based on general solution of sine function.

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Q: Obtain the unique solution for x3 + 4x2 - 10 = 0 on the interval [1,2] by Secant Method.

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Q: lex. min. {g, (x), g₂ (x)} 9₁ (x): -2x1 - x₂ ≥ 9 92 (x): X₁ X1 - 2x₂ ≥ 10 st. 2x1 + 5x2 ≤ 16 6x₁ +…

A: