Consider the initial value problem: ty" - 2t2y" + 3ty' - 3y = t², y(1) = 1, y' (1) = 0, y" (1) = 1 The approximation of y' (1.2) by using Euler's method with h = 0.1 is most nearly: O 0.25 O 0.28 0.26 WA Business 0.27

Q: Use the improved Euler’s method to solve y' = 1 + y,   y(0) = 1, on the interval 0 ≤ x ≤ 1, starting…

A: Given: y'=1+y,  y0=1; 0≤x≤1. We have to compute the approximations using the improved Euler's method…

Q: 4. (D² +D-1)² y =0 ,when x= y = 0, y' = y" =1, y" = -1

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Q: find in Euler's way 2x ! y(0.1) de y(0)=1 , h=0.05 y' = y -- y

A: The general form for Euler's method is given by yn=yn-1+hfxn-1,yn-1.

Q: Use Euler's method with h = 1/4 to compute approximate values of y(1) for t.y'= y(sint), y(0)=2.

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Q: 8. The estimated population (in thousands) of a colony of penguins in Antarctica is modeled 6t+30 by…

A: Simple calcuation is done for first part and for second part divide differentiation formula is used…

Q: Use the one sided Greens function to solve the I.VP. -1 2 In 12, y(1) =0, y'(1)=1 412 y" +8ty' + y =…

A: Given equation is, For solving homogenous equation, By cauchy euler equation,

Q: Use Euler method to approximate the value of y(0.1), given y' - x2 - y = 5, y(0) = 3 with Ax = 0.025…

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Q: 5. Solve the initial value problem below for the Cauchy-Euler equation. ty"(t) + 10ty'(t) + 18y(t) =…

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Q: 2. Used Euler's method to approximate y (0.5) and y (1) for the I.V.P y' = y + xe2x, y(0) = 1.

A: Given y'=y+xe2xand y0=1

Q: no. 3

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Q: What is the value of the arbitrary constant C if the given DE is y' = 2(2x – y) which passes through…

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Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

Q: 5. Solve y'=x +y given y(1) = 0. Find y(1.1) and y(1.2) by Taylor's meth- od.

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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: 21. y' - 2y = f(x), y(0) = 1, where 1-x, 0, f(x) = if x < 1, if x ≥ 1.

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Q: Solve the initial value problem y" + 12y' + 37y = 0, y(0) = 1, y'(0) = 0 O y = 6e-6'cost + e-6f sint…

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Q: Find an approximation of y(1) using Euler's Method and h=.2 for dy/dx =4x-3y , y(0)=1

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Q: Find the general solution using variation of parameters. - 4y + 4y = (x + 1)e²-

A: To solve the following problem

Q: Q1: Solve the ODE eq. y" + 3y - 4y = 4cos3t, where y(0) = 1 and y'(0) = 3

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Q: Q.4 Use the one sided Greens function to solve the I.VP. -1 4t2y" +8ty' + y = 3t 2 Int2, y(1)=0,…

A: Introduction: Green's function is a process to determine particular solution of a higher order…

Q: Find the solution of xy" + 5xy +(4 – Ix)y = 0, x > 0 of the form where co = 1. Enter n= 1,2,3, ...

A: Let the solution of the above differential equation is given as: y=xr∑n=0∞cnxny=∑n=0∞cnxr+nThe…

Q: et y" +5y' +y= xe* the particular solution of the equation can be obtained: elect one: a. By both…

A: The given differential equation is -  y'' + 5y' + y = x-3ex

Q: Q2: (a): Solve (i) (x² D² – xD – 151I)y = 0 y(1) = 0.1, y'(1) = -4.5 (ii) 100 – 20 + d? N dN dt? dt

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Q: Solve 2y"-5y+3y=0, y(0) = 1, '(0) = 2.5 (Note: The characteristic equation does factor.) y(t) =

A: Step 1: The given differential equation is, 2y"-5y'+3y=0 It can be written as, 2D²y-5Dy+3y=0 (Here…

Q: 17. Solve the IVP: y" + 8y(v)? = 1, y(1) = 4, y'(1) = 1/4. Describe the procedure thoroughly and…

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Q: x' = 20 t3 x, x(O) = 2 x(0) = 2 Solve the above IVP and then find x(0.8). Put x(0.8) accurately…

A: We have to solve given initial value problem:

Q: Exercise 2.2.9: Solve y" +9y' = 0 for y(0) = 1, y'(0) = 1.

A: 2.2.9 Given that the differential equation is                                       To find the…

Q: (b) Find the open t-intervals on which the particle is moving to the right. (Enter your answer using…

A: The solution for "b" is given below:

Q: Let u(g) and v(g) be the Fourier transforms of u(x) and (2) of the product u(z) v(x)? Select one: O…

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Q: Use Euler method to approximate the value of y(0.1), given y' - 4y = 3x2, y(0) = 5 with Ax = 0.02

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