Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₂ using the followingvalues.A =·15x(t) =5 - 261 -5f(t) =[3]x(0) =00Atcost + 5 sin tsint...- 26 sin tcost-5 sint

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Answered: Use the method of variation of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Curves 4. Find the derivative y' for each of the following or functions. You do not need to simplify your answers. Now you can choose which method you want to use to find the derivative. Show work a. _y= C. b y = (e ² + 4x²¹³) (2 + √x ) x - 2x)+5x4 y= 2x² - 4x+1 7x+4
1) Find the derivative of f(x)= 2x° + 2x+12. Then evaluate the derivative at x=1andx= 4. 2) The distance a particle moves along a path is defined by s(t)=6t–2 +4, where t is given in seconds and the distance of the particle is given in millimeters. Find the expression for the instantaneous velocity v(f) of the particle. 3) The height h in meters of a person jumping off a trampoline can be defined by h(t)=0.3+3t –²on the interval 0, 3], where time t is. given in seconds. Find the maximum and minimum heights of the jump.
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4. (a) Do 3 steps numerically using Heun's method. Show details. (P +1) y + 3ty = 6t, y(2) = 0, h = 0.1 (b) A "three-point formulas" for the derivative is
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1. Candace tried to find the derivative of the function y = h(x)e-4f(x) but her group members disagreed with her result. What did she get right? What did she get wrong? Correct her y' = h'(x)e-4f(x) + h(x)e-4f(x) (-4) work. After figuring out her error, Candace attempted to check her solution by rearranging the right side of the equation y = h(x)e-4f(x) into a fraction and using the quotient rule to differentiate. Verify the correct solution using this method.
9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7
After 25 years, your savings account has now grown to $16,200 and has an interest of 6.1% that compounds continuously. How much did you deposit at the beginning of the account
3. Explain two different ways to solve for the derivative of s(0) = -5cote and show all steps for each method. (Hint: They are both similar but require different derivative rules.) a) Method 1 b) Method 2 [C/4] [C/4]

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Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₂ using the following values. A = x(t) = 5 - 26 1 -5 f(t) 4t 3 x(0) [:] cost + 5 sin t - 26 sin t sint cost-5 sint ...