Use the fourth-order Heun and Runge Kutta methods to approximate the solution to the problem dt = 2² +²et interval t on the 1≤t≤ 3 with h=0.1 subject to the initial value y(1)=0 compare your approximations with the solution exact y(t) = ² (et - e)

Q: You have been given the following: x=y-x+t x(0)=6 y(0)=2 y'=y Solve it and write you answers in the…

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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: X1 - x2 +1 = 0) 1. Solve : x,? + x,² = 4 } with seed values x1(0) = 0.8 and x2(0) = 1.8. Compute up…

A: x1 - x2 + 1 = 0  =>  x1 = x2 - 1  x12 + x22 = 4 =>  x2 = (4 - x12)1/2    x1(0) = 0.8, x2(0) =…

Q: dy Solve the initial-value problem for y as a function of x. (16-2²) d = 1, y(0) = 9 y +9 X

A: The given initial value problem is:

Q: For which of the initial approximations  x1 =a, b,c and ddo you think Newton’s method will work and…

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Q: Use variation of parameters to find a particular solution of y" - y =

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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: Use fourth order Runge-Kutta method to solve numerically the follewng initial value problem -100 exp…

A: According to Runge-Kutta  Fourth Order Method, for differential equation  dydt=f(y,t)…

Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: Determine (without solving the problem) an interval in which the solution of (9-1²)y + 2ty = 4t²,…

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Q: The area, A km², of an oil spillage is growing in time t hours according to the DE dA dt = 4et √Ā'…

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Q: 3. Approximate value of the root of the given equation f(x) = – 3x + 5x + 14x between 2 and 3 within…

A: The given problem is to find the approximate root using secant method in between 2 and 3 with Ea=0.…

Q: Q3- Solve only one of the following: A- Find the approximate solution for the function y' x + y…

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Q: What is the particular solution if y(1)=0? 1/2 xy = y + (x² + y³)"

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Q: [  y'''- y' = ex - 2x  ] Please find a particular solution yp for the above.

A: Particular Solution: Consider the equation Let be the differential operator Then equation (1) can…

Q: Q2 (a) Determine the solution of y" – y = e2x – x + sin x using method of undetermined coefficient.…

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Q: t3y'''+3t2y''=1.  Use Variation of Parameters to solve this problem. Three solutions to the…

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0