. Consider the initial-value problem y'= 0.1!y+0.4x², y(2) =4. Use Euler's method to obtain the approximation of y(2.5) using h=0.1 and then h=0.05.

Q: Use the method of variation of paran solution to the given equation. - 2x y'"' + 6y'' +12y' + 8y = e

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Q: Use h = 0.1 and Heun’s method to find solution to y'' + 3y' = 12 with y(0) = 5, and y'(0) = 1.…

A: Given: Use h = 0.1 and Heun’s method to find solution to y'' + 3y' = 12 with y(0) = 5, and y'(0) =…

Q: 4. Solve the particular solution of y" + 3y' + 2y = 6e¬, y(0) = 1, y'(0) = 2, using a. Variation of…

A: we have given the differential equation y"+3y'+2y=6e-ty(0) = 1, y'(0) =2 we have to find the…

Q: y" – 2y + y = 1+x?

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Q: Apply Euler's method twice to approximate the solution to the initial value problem on the interval…

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Q: Apply Euler's method twice to approximate the solution to the initial value problem on the interval…

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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: 1. Use (forward) Euler's method to approximate the solution of the IVP y' = −3y, y(0) = 1 on the…

A: y'=-3yy0=1∆t=0.2

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 with each of the following step sizes to estimate the value of y(1.6), where y is…

A: Use Euler's method with each of the following step sizes to estimate the value of y(1.6), where y is…

Q: (a) (2e – x)y' = 1.

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Q: Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference…

A: This question is about application of numbers theory

Q: 1 Obtain a numerical solution of y-1 = using Euler's method with step size equal to (0.02) y and…

A: Given 1yy'-1=x3y

Q: Use Euler's method with n = 5 to estimate y(3.5), where y(t) is the solution of the initial-value…

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Q: Q3: Solve the following 0 2

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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: Find the values of "r" for which y(x) = e* solves the equation y" +3y'-4y= 0

A: We have to find the value of r .

Q: x" +3x' +2x = t?+ 29 e", x(0) = 1, x'(0) = 2 Solve the IVP and find x(0.25) to at least four decimal…

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Q: Q4. Solve numerically by using Runge-Kutta method y' =√xy+1 with y(0) = 1 to find y(0.05 and h =…

A: 4. Given,                  y'=xy+1;    y(0)=1.  To find the value of y(0.05) and h=0.025.

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. Compute the true solution to the problem Y' (t) = -e-Y(t), Y(0) = 1. Using Euler's method, solve…

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Q: Use the explicit Euler and Runge- Kutta methods to estimate y(2) if y(t) is a solution to y' = 1/…

A: For calculations only take t as x. Given y′=1x2+y, y(0)=1, h=0.2, y(2)=?Here, given is…

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: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

Q: 8. Using the Runge-Kutta method of the fourth, solve y" = y + xy', y(0) = 1, y'(0) = 0 to find…

A: We take y'=z the Given equation is y''=y+xz,y(0)=1,y'(0)=0,y(0.2)=?…

Q: Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the…

A: Step size

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 6. A small metal bar, whose initial temperature was 20°C, is…

A: Given,Initial temperature is .Then,Then, by the formula of of Newton's law of heating we…

Q: d®y dæ 3 y (0) y' (0) 1 y" (0) = 0 ||

A: Let us consider the differential equation L[D]y=Q(x) Particular solution for the differential…

Q: 3. Use the Newton-Raphson method and the modified secant method (8= 0.05) to determine the root of…

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