Answer the following question Q1:-Using Euler method to find y (2) using h=0.5 for y' = , y(0) = 1 Q2:-Using Rung-kutta method (R4) to find y (0.5) using h=0.5 for y' = -y in y ,y(0) = 0.5 %3!

Q: x²=-2x+4y y = -4x-2y wh x(0)=2, y(0) = 8 At=01 9+0 2100 JFF Use the Evien Method with a time step of…

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Q: Which of the following is a particular solution of the equation y"+y'+7y=4cos2x? O a.…

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Q: 1. and X = 2. %3D Find at t =2

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Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

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Q: 9(a). Suppose that in the "water and plant growth height" example we have four plants in the…

A: The following information has been given: 9(a.) x y 1 6.4 2 6.6 3 7.6 4 9.4 9(b.)…

Q: 2. the approximated roots for equationf(x) = e* - 3x in intervals [1,3] is found to be 1.34 find the…

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Q: Eg(i)x' where | x|< 1. What is g(i)? (1-x) 1 Let G(x) = %3D %3D i=0

A: Introduction :

Q: Even if the error terms in the regression equation, H1,H_2,....,µ_n, are not normally distributed,…

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

Q: Q2:- Find the domain and the range of the following equations:- (1)W = (2)W = sin x y (3)W = xy (4)W…

A: Find the domain and range of the following. Note- Since multiple questions are asked, I will answer…

Q: 2. y" - Зу' +2у %3D е** + 6х3 — 2+ 3sin(4x)

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Q: Given f(20) = 6, g(20) = 10, f'(20) = – 16, gʻ(20) = 15. Answer the questions below: %3D %3D a) k(x)…

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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: LET F(X) =2 x SIN(X), = 2 x 10" TIMUM STEP VALUE THAI CAN BE USED WIIH CENTRAL- DIFFERENCE FORMULA…

A: We know that the optimal step formula for the given value of epsilon and the upper bound M is given…

Q: y + 5xy + y = 6 In x + 4 where y (1) = -1, y (1) = 1 -1 +x - + 20 ... 7x5 -1+ 주 - (x-1)4 + 12 (x-1)7…

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

Q: Using Monte Carlo, estimate the value of e*y dx dy. 0.

A: Given that, ∫01∫01exydxdy By the monte carlo formula, ∫01∫01exydxdy=∫01exyy01dy=∫01eyy-1ydy

Q: • Consider the (nonlinear) initial value problem =-2y. y(0) = 9% • Does it have a solution for a) 36…

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Q: What was the 1-hour growth factor for the bacteria's mass?

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Given that f(1)=2, f'(1)=-3, g(1)=6, and g'(1)=3 find h'(1) for h(x) = f(x)g(x). %3D O-12 O-24 -6-

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Q: a) Exaluate: %3D :(?)6 puo (x puif (9 and (3 +x x <O %3D for which f (x)=9). Give exact working out…

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Q: Apply Euler method and Richardson extrapolation for h = 0.2, 0.1 the problem: and abtain g y' = ty…

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Q: If q x2 yz3 %3D =, the small increment in q with &r=8y=8z=±0.1 can be approximately calculated by…

A: We will use partial derivatives to calculate the required quantity.

Q: 1.4 If f(x)=(2x+2)(x+3) and g(x)= 4x+3 1.4.1 For which value of x is f(x)be non- real? 1.4.2 Solve…

A: The given functions are: f(x)=(2x+2)(x+3)=2x2+8x+6g(x)=4x+3

Q: 4.2.11 Find (fo g)(x) and (g o f)(x). f(x) = 6x – 1, g(x) = 3 – 2x (fo g)(x)=(Simplify your ans %3D

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Q: 3. Solve the following equation by secant method, using the range (-1, 1). F(x) = 2 cos(x) –…

A: Lets solve the problem using secant method

Q: If g(t) = 2t* + 3t2 - 5 find g(0) = a'(0)

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Q: 5) Consider the initial value problem and the following data y = (x + y)/2, y (0) = 2 x 0.0 0.5 1 y…

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Q: 6.23. Is it possible to solve y' = xy for y(0) = 0? Is the solution unique? Can you find such…

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Q: Solve the following initial value problem. y®) – 2y" + y' = 2 + 3xe*; y(0) = y'(0) = 0, y'"(0) = 1…

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Q: Find L(y). / + 2x = 2 - x' = et (0) = x (0) = 0 -2 L (y) PL(y) = %3D s(s2 +2) 2s L (y) = %3D…

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Q: Q.1 Solve the following B.V.P. y" – y = 2e", y(0) – 2y'(0) =-1, 3 y(1)– y'(1) = e.

A: See the attachment

Q: n) Find The (x) -V

A: The objective is to find the general solution of differential equation xy''+y'+xy=0 on 0,∞.

Q: Consider the following 1" order initial value problem: with y(0) = 1 (E) Which of the following…

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Q: 10. Given that f(x) = 3x + 7 and g(x) = , what is the %3D %3D value of f(g(4)) ? F. 8 G. 19 Н. 31 J.…

A: Given that f(x)=3x+7 and g(x)=x22   To find: f(g(4))

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.