Solve the following initial value problems. When it is possible, express the solutions explicitly in terms of the independent variable.
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Solve the following initial value problems. When it is possible, express the solutions explicitly in terms...
B1: (24 marks) Solve the following initial value problems. When it is possible, express the solutions explicitly in terms of the independent variable. a) (t? + 1) 44 +3ty = 6t, y(0) = -1 b) * = y(1 – y), y(0) = 1/2 c) dy + +y = ty?, y(1) = 1 - 4y = 3e2t, y(0) = -2, y'(0) = 0
4. Solve the following initial value problems and sketch the solutions: (a) 4y" – 4y' + y = 0, y(1) = -4, y'(1) = 0 (b) y" + y' – 2y = 0, y(0) = 3, y(0) = -3 (c) y" – 2/2y' + 3y = 0, y(0) = -1, y(0) = V2
Use Laplace transforms to solve the following initial value problems. Where possible, describe the solution behavior in terms of oscillation and decay. y′′ +4y = δ(t−1), y(0) = 3, y′(0) = 0.
Question 5: (17 points) Use Laplace transform to solve the initial value problem V" - 4y + 4y = 2.814 -- 3)y(0) = 1, (0) = 2 (If you use convolution theorem for an inverse Laplace transform, you need to compute the integral to express your answer explicitly in terms of t.)
Express the solution of the initial value problem in terms of a convolution integral. (Do not evaluate the integral. There will be an integral in your answer.) y" + 4y = g(t) y(0) = 1, y'(0) = 2
solve the given DE or IVP (Initial-Value Problems) In Problems 2-5, solve the given DE or IVP (Initial-Value Problems) 3. y sin2 (4x - 4y +3)
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
please answer all these questions and show all working 2. Solve the the following initial value problems. (a) 9y" – 12y' + 4y = 0) with y(0) = 2 and y'(0) = -1 y" + 4y' + 4y = 0) with y(-1) = 2 and y'(-1) = 1 (c) 4y" + 12y' +9y = 0) with y(0) = 1 and y'(0) = -4 (d) 4y" + 4y + y=0 with y(0) = 1 and y(0) = 2 (b)
Problem D Solve the following initial value problems using the Laplace Transform. To receive full credit, every time you use LAPLACE TRANSFORM FORMULA indicate which one you used 1. y' – 3y = te3t, y(0) = 1 2. y" – 4y = eat, y(0) = 0, y'(0) = 1 3. y' + y = H(t – 5), y(0) = 2
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0) = 8, y'(0) = 0 b) y" + 6y' + 13y = 12e-3xsin(2x), y(0) = 0, y'(0) = 0 (10 point) Find a general solution of each of the following nonhomogeneous equations. a) y" + 4y = 12x−8cos(2x) b) y(4)− 4y" = 16+32sin(2x)