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18-25 SOLVING INITIAL VALUE PROBLEMS Using the convolution theorem, solve: 19. y" + 4y = sin...
10. Solve the initial value problem using Laplace transform ( 14 points) y" + 4y =...
10. Solve the initial value problem using Laplace transform ( 14 points) y" + 4y = 2 sin(3t) with y(0) = 1 and y'(0) = 1
17. Use the Laplace transform to solve the initial value problem: y" + 4y' + 4y...
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.
Using the Laplace transform, solve the initial value problem 8. y(0)-0. y" + 4y-sint-u2" sin(t-2r), y(0)-0,
Using the Laplace transform, solve the initial value problem 8. y(0)-0. y" + 4y-sint-u2" sin(t-2r), y(0)-0,
4. Solve the following initial value problems and sketch the solutions: (a) 4y" – 4y' +...
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
Question 5: (17 points) Use Laplace transform to solve the initial value problem V" - 4y...
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.)
(10 point) Solve the following initial value problems. a) y"+ 4y' + 8y = 40cos(2x), y(0)...
(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)
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x...
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...
Use the Laplace transform to solve initial value problems 5. *" + 4x = f(x); x(t)...
Use the Laplace transform to solve initial value problems
5. *" + 4x = f(x); x(t) = 35. f(t – 1) sin 27 dt, x(0) = x'(0) = 0 (use a convolution theorem).
Use the convolution theorem to obtain a formula for the solution to the initial value problem....
Use the convolution theorem to obtain a formula for the solution
to the initial value problem.
y ′′ + y = g, y(0) = 0, y′ (0) = 1 , where g = g(t) is a given
function.
1. (10 pts) Use the convolution theorem to obtain a formula for the solu- tion to the initial value problem y"+y=g, y(0) = 0, y'(0) = 1, where g = g(t) is a given function.
Note: Use partial fractions when solving Use the Laplace transform to solve the following initial-value problem....
Note: Use partial fractions when solving
Use the Laplace transform to solve the following initial-value problem. y" +5y' +4y = 20 sin 2t, y(0)=-1, y'(0) = 2
10. Solve the initial value problem using Laplace transform ( 14 points) y" + 4y = 2 sin(3t) with y(0) = 1 and y'(0) = 1
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.
Using the Laplace transform, solve the initial value problem 8. y(0)-0. y" + 4y-sint-u2" sin(t-2r), 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
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.)
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...
Use the Laplace transform to solve initial value problems
5. *" + 4x = f(x); x(t) = 35. f(t – 1) sin 27 dt, x(0) = x'(0) = 0 (use a convolution theorem).
Use the convolution theorem to obtain a formula for the solution
to the initial value problem.
y ′′ + y = g, y(0) = 0, y′ (0) = 1 , where g = g(t) is a given
function.
1. (10 pts) Use the convolution theorem to obtain a formula for the solu- tion to the initial value problem y"+y=g, y(0) = 0, y'(0) = 1, where g = g(t) is a given function.
Note: Use partial fractions when solving
Use the Laplace transform to solve the following initial-value problem. y" +5y' +4y = 20 sin 2t, y(0)=-1, y'(0) = 2
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