1: Find the solution of the following Differential Equations 1. dx2 + y = 6e* + 6 cos(x) d'y 2. dx2 dy 4 +3y = ex +2 dx d?y 3. dx2 dy - x = 0 dx

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Q: 8. Let (X, d) be a metric space, and A, B are subset of X, then (i) Fr(A) = A n (A)° A – int A (ii) ...

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for you...

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Q: C01. Verify that for all n>1, the Sum the first 2n positive of the squares of hitegeis is giveń baf ...

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you...

Q: Find the radii of curvature and torsion at a point of the curve r? + y2 = a², x² – y? = az. %3D %3D

A: Given curve is x2+y2=a2x2-y2=az

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Q: A clamped beam of length 3 is modeled by: y(4) = 24, y(0) = y'(0) = 0, y(3) = y'(3) = 0. Solve the p...

A: The given differential equation is y4=24, with y0=y'0=0 and y3=y'3=0 Now we integrate the given equa...

Q: 2 Consider the IVP (x + 1)²y" – 2y = 0, y(0) = 1, y'(0) = -1. Determine all ordinary points of the d...

A: Since you have asked multiple questions, we will solve the first question along with its subparts fo...

Q: Solve the ODE: (x² – y²e² )dx + (x² + xy)e#dy = 0.

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Q: (c) Calculate the population of a spherical cloud of locusts which lies in the ball x2 + y?+ (z – 1)...

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Q: Q5. If the area of the below region (R) equals to (6.25 m2) and if you know that the height of the t...

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Q: Re-write. the.ethar.five.iterated.nt.eg.ral.s. 2 Fang, z)dydzdx -I x2 d

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: What is 2+4

A: The value of 2+4 is 6  

Q: Show that the eigenvalues of the Sturm-Liouville system dy + Ay = 0 dx? y(0) = 0, y(L) = 0 %3D gre a...

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Q: What is L! if 2 1 +. s s-4] 4r A. -2t +e В. -t+ 2e¬7! 3t +e" D. -2t+e" C. 47 3r E. 4t - 2e"

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Q: cos ( - i ln3) is equal to, COS O 4/2 O 5/2 4/2 2. O 5/2 6. 4/2 23,

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Q: The solution of the differential equation y" – xy' + y = 0 is y = ce¯* + cze2* y = 1- x? D This opti...

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Q: An investor wants to save money to purchase real estate. He buys an annuity with quarterly payments ...

A: Solution

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A: We have to find the transformed equation using an adequate substitution.

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Q: [9] Suppose x is a particular real number, and let p, q, and r symbolize "-1 <x," “–1=x," and “x < 5...

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Q: Find the volume of the solid enclosed by the paraboloids z = 1 (x2 + y²) and z 32 – 1 (x2 + y²).

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Q: A topological space (X, t) is a T1-space if and only il for each x e X, the singleton set {x} is clo...

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Q: 3. Calculate the following integrals over the given C curves by using the Cauchy integral formula. e...

A: The given problem is to evaluate the given complex contour integrals over the given region using cau...

Q: Question 2. Let G be a finite group, H < G, N 4G, and gcd(|H|,|G/N|) = 1. Prove that H < N.

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Q: rate

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Q: Assume A, B, and C are sets. Prove the following deductions are valid. a.  A ⊂ (B ∪ C), ∴ (A \ C) ⊂ ...

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Q: 6. (Sections 8.8 and 8.9) Determine whether the following piecewise-defined function is a probabilit...

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Q: Use Taylor series for y(x + h), y(x – h), y(x + 2h), and y(x – 2h) to derive the FD formula for the ...

A: Here we have to use taylor series for y(x+h) , y(x-h) ,y(x+2h)  and y(x-2h)   

Q: By applying Rolle's theorem, check whether it is possible that the function roots. Answer: ?

A: The given equation is f(x)=x9+x-6 f'(x)=09x8+1=09x8=-1 If f(x) has two real roots then By Rolle's th...

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Q: 1 3 -1 5 9. Let A = -1 0 -2 -2 1 1 1 3 (a) Find a basis for the row space of A. (b) Find a basis for...

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Q: n 3. Suppose G is a group with order 99. Prove that G must have an element of order 3.

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Q: "The product of two negative real numbers is positive" Is given by? Select one: O a. 3x Vy (x 0)) O...

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Q: 4. Determine the solution for the system of linear equations below using any method applicable: x + ...

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Q: 3. Evaluate (2 - )(-3+j4) in exponential form

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Q: Find the eigenvalues and suitable bases to write the following complex matrices in their Jordan norm...

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: [9] Let A = {a, b, c, d} and B = {1, 2, 3}. Define a function F: A → B as follows: F3(а, 3), (b, 3),...

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