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1. Solve the equation y" + 4y' + 5y = 0 with the initial conditions y(0) = /2, y'(0) = -5.
Question 1: [25 pts] Consider the IVP y" – 4y' - 5y = 0, y(0) = 1, y0) = 2. a) Find the solution of the given IVP using the corresponding characteristic equation. b) Find the solution of the IVP using the Laplace Transform. c) Does the solution change if we would change the second initial condition as y'(0)=3? Explain.
17. Use the Laplace transform to solve the initial value problem: y" + 4y' + 4y = 2e-, y(0) = 1, (O) = 3. 18. Use the Laplace transform to solve the initial value problem: 4y" – 4y + 5y = 4 sin(t) – 4 cos(1), y(0) = 0, y(0) = 11/17.
5. Find the general solution of the following differential equations: (a) 6"-5y y 0 (b) 4y"+12y9y 0 (c)2" 3y 6. Solve the following initial value problems:
Question 5 < > Given the differential equation y' + 5y' + 4y = 0, y(0) = 2, y'(0) = 1 Apply the Laplace Transform and solve for Y(8) = L{y} Y(s) = Now solve the IVP by using the inverse Laplace Transform y(t) = L-'{Y(s)} g(t) =
Solve the initial value problem y" – 4y' + 4y = 0, y(0) = -3, y'(0) = -17/4
Given the differential equation y"' + 5y' – 4y = 4 sin(3t), y(0) = 2, y'(0) = -1 Apply the Laplace Transform and solve for Y(s) = L{y} Y(s) = 1
#32
U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
Use the LaPlace transforms to find the solution to y''+4y'+5y=∂(t-2π) y(0)=0 and y'(0)=0
Question 4 a) Solve y```` -4y```-5y``+36Y`− 36