PROBLEM 2 Prove the following: (a) E (Č X) = C E(X) (b) E (X + Y) = E(X) + E(Y)

Q: Problem 1: [(4x + 3)²D² − 12 (4x + 3)Dx+64]y = 16[(4x + 3)² sec² (ln|4x + 3)] - Problem 2: x³y"" −…

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Q: Problem 4. Fill i in the previous pr Y X a 0.1 b 0.1 0.1 d. 0.05 e f

A: The marginal probability function for A is, outcome probability a 0.25 b 0.1 c 0.3 d 0.05…

Q: Problem. 1 Approximate y (0.4), f'(x,y) = x + 2y ,y(0) = %3D 0, and the step size, h = 0.1 %3D

A: We have to find the approximate value of y(0.4) using the differential equation with initial…

Q: Problem 5. Find solutions of the following equation satisfying the given initial conditions (solve…

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Q: Problem 5 Solve Cauchy Euler equation r'y" + ry - y = r'e

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Q: Problem 9 Solve the initial value problem: dy — хеУ-х; х 3D 0 апd y %3D 0 dx a. y = -In 2 + In(e*^2…

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Q: Problem 15  Evaluate the integral.  ∫(4x+0)/((x^2)-2x+10)dx Answer=________________ +C

A: Given

Q: Problem 3 Find the solution of the following initial value problem: [6 -1] x'(t) = 2x(e), x(0)=

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Q: Challenge Problems: (9) Show that the change of variable t = ar+b transforms the equation bo(a.r…

A: According to guideline , I am solving question number 9.For question number 10, please post the…

Q: Question 3 1 pts Evaluate 2x y+-3(zy) given a = 10 and y = -5

A: Answer is 155.

Q: 12.1 12.2: Problem 3 5 | f(x) dx = 3 and g(x) dx = –4, what is the value If -3

A: Given that: ∫45f(x)dx=3 and ∫-30g(x)dx=-4

Q: Problem 1 Find the value of C, so that the function y = C,er + Ce + 2 sin x satisfies the initial…

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Q: Example 11. Find a particular solution of equation ty" – 2ty' + 2y = t°e*. yUni 13 21

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Q: Question 8: Solve the following initial value problem: y" – 6y' + 13y 0, y(2) = 6, y' (1) = 9 %3| -

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Q: Problem 3.1: Find the GS of xyy' – y? = x/x? + (ay)² where a + 0 is any number.

A: given differential equation xyy'-y2=xx2+αy2now divide both sides by  xy ,we gety'-yx=x2y2+α…

Q: Problem 5 Solve Cauchy Euler equation r'y" +ry -y =r'e

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Q: Solve the following S-L problem y"(x) + Ay(x) = 0, y (0) = 0, y(L) = 0.

A: Given that, y''x+λyx=0y'0=0yL=0 We consider three cases according to λ so that we can get…

Q: Question 2 Consider the following IVP: x" + 4x = t+4; x(0) = 1, x'(0) = 0 Find the general solution.

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Q: 1 e* dx PROBLEM 2: J: 2 Inx e"dx PROBLEM 3 : PROBLEM 4 : re-3x²+1_ dx хе 4x PROBLEM 5: J Ine

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Q: Problem 4 Given that y1(t) et is a solution of the equation ty" – (1+t)y' + y = 0, use the method of…

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Q: Solve the S-L problem. y" + ay = 0 y(0) = y(1) & y' (0) = y'(1)

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Q: Problem 14. (1 point) f) de- f) dx = where a= and b= Note: You can eam partial credit on this…

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Q: * Problem 6: A mass spectrometer is being used to separate common oxygen-16 from the much rarer…

A: If a particle of mass m having a charge of e ( electronic charge ) enters perpendicularly in…

Q: Problem 5 Solve Cauchy Euler equation ry" + zy-y =r'e

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Q: Problem 1 - Find the solution of the DE y" − y' + 9y = 0.

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Q: Problem (1): Evaluate the fC 2x*e²* dx

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Q: Problem 13.3.5: Suppose heat is lost from the lateral surface of a thin rod of length L into a…

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Q: Problem 1. Discuss the existence and uniqueness of solution(s) of the following IVP: dy Vr - y +1,…

A: Given: dydx =x-y+1 , y(1) =0 To discuss existence and uniqueness theorem for given IVP

Q: -72=-1 Problem 2/ Solve the following initial value problems. 3) 7=-12 y, y=1, 9=3.5 when x=0 dx dx…

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Q: QUESTION 11 dz = = zP z1- -i (-e2 – 1)i e (e? + 1)i e (e? – 1) ei (e2 – 1)i e

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Q: Question 1 Solve the integral: Seln(2x²+3x-4)³ (4x+3)dx A eln(2x²+3x-4) (4x+3) 3(2x²+3x-4)…

A: To evaluate the given indefinite integral.

Q: Solve the following S-L problem y"(x) + Ay(x) = 0, y'(0) = 0, ul L) -0

A: This is a Sturm Liouville problem.

Q: Problem 2: Use the Improved Euler method (h= 0.1) to obtain a four-decimal approximation of y(0.5)…

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Q: PROBLEM 3: f (x) = Vx + 2 at (-1,1)

A: slope of tangent of function y=f(x) at (a,b) is given as m=f'(a)=dydxx=a

Q: Problem 7: Show that if r 0 approaches zero as t → o.

A: The logistic equation is mathematically given as.

Q: Problem 5. e(x) %3D D리1-3; r so.

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Q: Problem VII: Evaluate | ye"dx + xe" dy where C is the portion of the curve y =x' – x +1 from (0, 1)…

A: To evaluate the given integral , we use the green's theorem. According to Green's theorem: Let R be…

Q: A. In each of Problems 1 through 5, Use the method discussed under "Bernoulli Equations". 4. y'+=…

A: Standard form of first order Bernoulli differential equation is:…

Q: Problem 16 Show that the given equation is not exact but becomes exact when multiplied by the given…

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Q: Problem 2 f(x, y) = log(x² – y² + 1) (a) Find the definition domain Dof z=f(x,y) and draw it in…

A: OK

Q: question: 3. The Big Pot of Soup. As part of his summer job at a restaurant, Jim learned to cook up…

A: Given Data: As part of his summer job at a restaurant, Bren learned to cook up a big pot of soup…

Q: Problem # 64 For what value of k is the following a spline function? ka² + (3/2), { z² +z+(1/2),…

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Q: Problem 3. Sketch the slope field for the equation y' = yx³ + x² at given points -2 -1 1

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Q: Problem 3 Using Variable Separable, solve x² (y + 1) dx + y² (x - 1) dy = 0

A: Given differential equation is x2(y+1)dx + y2(x-1)dy = 0

Q: 4. limr→1 e-1_1 x-1

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Q: Solve the Sturm liouville problem 2. x yu + X y' + (16+x)y = 0 ४ पुल्टी:

A: Answer

Q: Solve th e following problem (1): y'+y'-2y= 0; (2): y" -6y'+9y 0; (3): y"-10y'- 24y 0; |(4):…

A: No1               y'' + y' - 2y =0       The axullary equation is            m2 + m - 2 =0       ⇒…

Q: Problem. 9: Let z = a -7 xy+ 6 y? and suppose that (x, y) changes from (2, 1) to (1.95, 1.05).…

A: We have to solve given problem: