Section 7.5

# Section 7.5 - Differential Equations Math 308 Spring 2008...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Differential Equations Math 308, Spring 2008 Texas A&M University c F. Dos Reis Section 7.5 Recall form the previous chapters: f (t) 1 eax tn n = 1, 2, sin bt cos bt eat tn n = 1, 2, eat sin bt eat cos bt F (s) 1 s 1 s-a n! sn+1 s2 s2 b + b2 s + b2 n! (s - a)n+1 b (s - a)2 + b2 s-a (s - a)2 + b2 L eat f (t) = L {f (t)} (s - a) L f (s) = sL {f } (s) - f (0). L f (s) = s2 L {f } (s) - f (0) - sf (0). L f (n) (s) = sn L {f } (s) - sn-1 f (0) - sn-2 f (0) - - f (n-1) (0). L {tn f (t)} (s) = (-1)n Exercise 1. Solve the initial value problem y + 6y + 5y = 12 et , using Laplace transforms. 1 y(0) = -1, y (0) = 7 dn F (s). dsn Differential Equations Math 308, Spring 2008 Texas A&M University c F. Dos Reis Method of Laplace transforms: To solve an initial value problem: 1. Take the Laplace transform of both sides of the equation. 2. Use the properties of the Laplace transfom and the initial conditions to obtain an equation for the Laplace transform of the solution and then solve this equations for the transform. 3. Determine the inverse Laplace transform of the solution. Exercise 2. (5p401) Solve the initial value problem w + w = t2 + 2, w(0) = 1, w (0) = -1 Exercise 3. (9p401) Solve the initial value problem z + 5z - 6z = 21 et-1 , z(10 = -1, z (1) = 9 Exercise 4. (35p402) Find a solution to the initial value problem y + 3ty - 6y = 1, y(0) = 0, y (0) = 0 Exercise 5. (27p 402) Solve the initial value problem y + 3y + 3y + y = 0, y(0) = -4, y (0) = 4, y (0) = -2 2 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Section 7.5 - Differential Equations Math 308 Spring 2008...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online