In this poblem wewill derive the loinomial thaorem. 3. a)use separaton of variablas to solve the ihrtial value probleen- (4X)y-ay 0) Find the paver senes solution of the initial vaie probum e l 11 (tXIy y C) Explain why this shows (Itx +axt ala-x (a-1(a-2) + 171x1 3! 2 1 d) Show that if ne Nthis gives where 20 n! k! (n-K)

Q: The solution of the 2" order IVP y" - y = 0, y(0) = 0 and y' (0) = 1 is

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Q: 3, Find the poner sertes solution in poners of (x-1) of *最+y=o; 0 2 +2y=0j つ4 4(メー)-4(メー)れ +…

A: Given that xy''+y'+2y=0 Take y=c0+c1(x-1)+c2(x-1)2+c3(x-1)3+c4(x-1)4+c5(x-1)5+.. Take the derivative…

Q: 2. Solve the DE, = using the homogeneous method. (a) Hint: Rewrite the RHS as 2 – (2)²

A: To solve the homogeneous differential equation

Q: (3) Solue the Initial Value Probles -that SatieSFies the Compleme equation (+) yM -2(x+ Dy! 13 ! %3D…

A: We are given a nonlinear non-homogeneous second order ordinary differential equation, which we have…

Q: Q: Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z = 1 x- y+ 5z = -2 2x + y = 3

A: The given system of equation is  3x + 2y -z =1 x - y +5z =-2 2x +y =3

Q: Use Euler's Method with h=0.1 to approximate the solution to the following initial value problem on…

A: Given function is y'=9x2-yx-y2 initial condition is y(2)=-32 Using Euler method xn+1=x0+nh We have…

Q: Use Euler's method to approximate the solution to y' = y + 2t , y(-1) = -1 on the interval [-1, 1]…

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Q: (c) Using the method of characteristics, or otherwise, find the general solution to Uy +5Ux = 0.

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Q: To: find the dolution of given :- differ ential equation. Given, eg" Now, Comparing et"o with M(x,…

A: The given orange part is the first step to check whether the given equation can be treated as exact…

Q: Can you explain why (a) a solution of r*y" + xy' + (x² – µ²)y = 0 (1) is of the form y(x) = E Anx"+r…

A: We are given that, Now, we need to why the series forms are the different forms of (1) and (2).

Q: 5. Solve y' = te3t – 2y, for 0 <t < 1, with y(0) = 0 and h = 0.5 a) By Runge-Kutta (R-K)Method of…

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Q: Solve for x, y, z and w by Gauss elemination Method. Given: 12x-8y+6z+10w=26

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Q: Use method of variation of paramaters (VOP) to solve the following equation. what is the…

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Q: 1) Using Modified Euler's method, solve y'= xy2 + y given yo) = 1 if h= 0.1 to obtain y(0.1), y(0.2)…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Let y(x) be the solution of y' = y − 6x such that y(2) = 2. Using a step size of 0.5, set y0 =…

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Q: 8. Find the partic ular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: We have to find the particular solution of x2y''+xy'=1 ; y=0 and y'=12 when x=1.

Q: D. Verify if The relatum O y= xe' y= eco{ 2x) is a soluhon to yl-Gy'+13y=D0 is a solution to yl -…

A: For verification of the solution will find the respective derivative and substitute into the…

Q: ve by nanu with = 0.6. Suisn po c) Solve by hand with the classical fourth-order Runge Kutta method…

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Q: Using of fourth oxdese with Ringe-kutta method Solve dy (0)%3D1at 2. | 22 2. 2=0.2,0.4

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Q: 8.9. The volume V of the liquid contained in the spherical tank of radius r is related with the…

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Q: Use trapezoidal method to solve the IVP u(0) = 1 a) Prove that the approximate solutions is: 2-h, Yi…

A: Given: An initial value problem                                                       y'=-yy0=1…

Q: Q Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z 1 x- y+5z = -2 2x + y = 3

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Q: The solution of ë+w?x = fsin wt with initial conditions r(0) = 0 y a(0) = 0 is given by %3D %3D

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Q: The appropriate form forVthe method of underenmined coeerents was used to solve the DE y" + 3y +…

A: c NOT option is correct.

Q: Using the Euler's method with step size h = 0.2, approximate y(0.4) if %3D y = y? – 2.2, y(0) = 1.

A: The solution is given by using the Euler's method as follows

Q: 10. y"" + y" = 3 А. 3 В. Зх C. D. 3x?

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Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

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Q: Solve this equations by using homotopy analysis methods y"+y' ^(2)=0 with initial condition v'(0)=2

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Q: Find the complete solution of the DE y"- y'=4e¯* +3e* with the initial conditions that when x = 0, y…

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Q: A) Verify that y = C1 + ©2x* is a solution of the DE: z²y" – 3ry' = 0. B) Find a solution to the…

A: We have to find the solution of given homogeneous differential equation with constant coefficient…

Q: Apply the improved Euler method to approximate the solution on the interval (0, 0.5] with step size…

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Q: If yV2) is a fundamental set of solutions for the DE: t'y"-3y' +costy3D0 and if W(v,V2)(1) =2, then…

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Q: 6. y" – 2y' = e* A. 2e В. -2е C. e D. -e

A: Given that the non-homogeneous differential equation is       y'' - 2y' = ex

Q: it as a Bernoulm cquaion in the uependeht varlavic A. 0. 2x'y = y(y? + 3x). Solve by two methods.…

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Q: 3. Let u(x, t) be the solution to 5ætu, – ut = 0, u(x,0) = 3x², x > 0 - obtained using the method of…

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Q: Solve the @iven dif frerenticul equation uning the variables method of seperatio n of dy 4y+3

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Q: b. Solve by using variable separation method. = 0 ax2' ay2 Which satisfies the conditions, u(0, y) =…

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Q: Selve The following syslem liner of equations: 1+ 44-21= 8 -3n + 2y-6Z=6 5n+ Fy-52-6 Solve by Using…

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Q: 2. In each exercise, obtain the particular of solution. 2y-) dy = 0: when x= 0, y = 1 (3x +v) dy =…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: What values of α and A make y=Acos(αt) a solution to y′′+6y=0 such that y′(1)=2?

A: The solution of differential equation y’’+6y=0 is

Q: iven y' = y – t² + 1, Osts2, y(0) = 0.5 and N = 10. nen, using Euler's method, the approximation of…

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Q: 5. Solve y' = te3t – 2y, for 0<t< 1, with y(0) = 0 and h = 0.5 a) By Runge-Kutta (R-K)Method of…

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: 2. Estimate the solution at z 3 for 2r-y y0) -1 using Euler's Method with a step size of h=1. (a) 1…

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Q: Consider the 1* order initial value problerm: y' = f(t, y), 1St<4, y(1) = yo A certain method is…

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Q: Solve the non-homogeneous DE. Hint: Use method of undetermined coefficients. y(4) – y = 5; y(0) =…

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Q: (a) Find the general solution of the equation (x – 2) y dr 3(х — 1) -y3 1 - (x + 1) (b) Given the…

A: A first-order linear ordinary differential equation(ODE) is of the form y'(x)+p(x)y=q(x). The…

Q: 2ste-tds + (s²e-t – t)dt = 0

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Q: ydx + x(Inx - lIny - 1) dy = 0, when x = 1, y = e %3D

A: Given :     ydx+xlnx-lny-1dy=0,        when x = 1 , y = e that means y1=e

Q: - 15x = 3r³t is a de dt (Choose all applicable answers.) O Homogeneous equation O Exact cquation O…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.