1. Use Euler's method to approximate to approximate the solution of the initial value problem over the given interval and the given step size. Present your answer in a table. dy =√y, y(0) = 0,0 ≤ x ≤ 4, h = 0.5 dx

Q: Use three steps of Euler's method to obtain an approximate solution of: dy = dx 4* y subject to the…

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Q: x-1/2c (4) y = x sinh 2x – cosh 2x

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Q: Write the solution of the following D.E in term of convolution y-2y-2y = 8 t-cost +1…

A: The general solution to the homogeneous equation y'' - 2y' - 2y = 0 is y_h(t) = (c_1 + c_2t)e^(-t).…

Q: y" – 2y + y = 1+x?

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Q: Find the x-value where the relative maximum of y=ex4−x2y=ex4-x2 closest to x=0x=0 occurs. When you…

A: Given, y = ex4-x2 First  guess x = 0   We have to find the second guess using newton`s method.

Q: You are given a first-order D.E. = x2 + y³ . Suppose the solution y(x) satisfies the initial dx…

A: dydx=x2+y3  and y1=-1

Q: 3. Use Euler's method to approximate the value of = -2x3 + 12x2 - 20x +8.5 from x = 0 to x = 4. The…

A: Since you have asked multiple questions, we can solve first question for you. Also first question…

Q: Employ fixed point iteration to locate the root of f(x) = sin √x-x. Use an initial guess of xo = 0.5…

A: The fixed point iteration method uses the formula: xn+1=ϕ(xn) and to approximate the root of the…

Q: 5. (y – x + 3)dx + (x + y + 3)dy = 0; x = 1; y = 4. Solve in two different methods.

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Q: 3. Use Secant Method to determine the root of f(x) = Sin (V x ) - x where x > 0. Use up to 8…

A: Given function is- f(x)=sinx-x where x>0 We need to find roots of given function using Secant…

Q: 6. Solve the initial value problem: dx (x² + 2y²). = xy, y(-1) = 1 dy %3|

A: First of all write the given initial value problem in MDX+Ndy=0 form which is the homogeneous…

Q: Find the root of the equation f (x) = x³ – x – 1 using Muller's Method. = 1, x2 = 2, x3 = 1.5. Stop…

A: According to Muller's method If initial guess of root is x0, x1 , x2 , then next approximation of…

Q: Q2. Solve x = cosx for solution exact to 3D by Newton's method (with xo = 0) and bisection method…

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Q: Q4. Solve numerically by using the improved Euler's method dy-√√xy + 1 dx = 0 with y(0) = 1 for…

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Q: 2. 10 points Solve the first order initial value problem dy y(0) = -2 dx + 2y = 3e-*,

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Q: (x² + 1) d x + 3x(y - 1) = 0, y(0) = 7 + 1) ( ² 2 y = 1 + 6(x² +1)

A: The given differential equation is; (x2+1)dy/dx +3x(y-1) =0, y(0)=7.

Q: Question 5 Using Euler's Method estimate y(0.3) with step size h-0.1 given -t+2y, y(0)=1 Show ALL…

A: if we have differential equation dydt=f(t, y),  t0=a and y0=y(a)=b also step size h  then…

Q: 1. Use fixed-point method to locate the root of f(x) = sin(vx) – x Use an initial guess of xo = 0.5…

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Q: f(x)=S0pi/2(8+4cos(x))dx Solve using multiple-application trapezoid rule, with n= 2 and 4.

A: I find the solution in 6 decimal place