1. Given f(x,y) =1+0.25y-e* with y(0)=- in the interval [0, 1]. Solve the IVP by using 3 Euler's method for a) h=0.2. b) h=0.1.

Q: 2. Use Euler method to compute ys for the DE yy'=2x for y(1)=3

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Q: Use Euler's method and 4 steps to approximate y(1)

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Q: a) Show that y=e*is a solution of the linear D.E y'+y=0, and y =xis a solution of the nonlinear D.E…

A: Please find solution of both parts.

Q: 2. Find the root of f (x) = 2* + x³ – x = 0 by using Newton Raphson method with initial value po=…

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Q: (f) dx /3 — 2х — г?

A: Question f,Given,           ∫x3-2x-x2dx

Q: 3y = /2y – 1, y(1) = 1. ) Find the solution y = y(x) of this IVP. Please present your solution y =…

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

A: Solution:

Q: 11.) Use a numerical solver to approximate y(1) for y' = 2xy², y(0) = 1 using Euler's method with h…

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Q: Given the initial condition y(0) : e–2y = y'? 3, what is the particular solution of the equation…

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Q: titution: 4 11 8 }]ÿ. y(0) = [¯²]. etermined coefficients: 12 -1 · [¹² −¹5]y+[e²].

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Q: 20. g(n) = (3x – 2)(4x' + 1) 22. f(1) = cot (2r) 24. S(x)=

A: solution is given below

Q: Use Gauss-Seidel method to solve for x, X,, Xạ until the relative error falls below 5% Repeat with…

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

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

A: In this question , we will find the approximate solution of the differential equations by using…

Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: The function y =x is one the solution of (x-1)y-xy'+y= 0. we use reduction to order method, second…

A: Given y=x is one solution of x-1y''-xy'+y=0. Let, y=vx be another solution of the given equation.…

Q: 2- Solve the following equation: Utt = c?uxx +, u(0, t) = u(2, t) = 0 u(x,0) = x? ,u; (x, 0) = e*

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Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

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Q: Find the form of yp to use in the method of undetermined coefficients y"-3y'-4y=x²e*+xe* a.…

A: Our objective is given below:

Q: State the maximum interval over which the solution  is valid.

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Q: Find the solution of the IVP x" - x' + 5x = 4+ u₂(t)e-2(t-2) x(0) = 2, x'(0) = -1 where u₂(t) is…

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Q: 21. Find particular solution of the differential oquation-2(x+ 1) Y.given x 0,

A: Givne that  The differential equation  To find the particular solution of the differential equation

Q: Solve for the integrating factor * y (x + y) dx + (x + 2y – 1) dy = 0

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Q: y' = (1-x²)y , y(1) = 1, h = 0.1 1.0921 1.0986 1.0974 O 1.0935

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Q: Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated…

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Q: Use Euler's method to approximate the solution to y' = 2ty – 2 , y(-1) = 2 on the interval [-1, 1]…

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Q: Of the solutions to the three di↵erential equations above which one is increasing at (1, 1)? Explain…

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Q: 9. Which of the following equations are separable? Write those that are separable in the form y' =…

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