Lecture 6 Notes

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Unformatted text preview: uations Ax = b . 5 2 x2 + x3 = and x3 can be whatever. 3 3 5 2 x2 = − x3 + 3 3 • Example 3. Solve the equation 1 • so x1 − x3 = 3 1 x1 = x3 + 3 2 and 3 2 3 2/3 1 ￿ x = C −5 + 2/3 0 3 the general solution to the homogeneous problem one particular solution to nonhomogeneous problem Solutions to nonhomogeneous differential equations Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). first order DE Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). first order DE second order DE Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). first order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). first order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). first order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). 3. The general solution to the nonhomogeneous problem is their sum: y = yh + yp = C1 y1 + C2 y2 + yp Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). first order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). 3. The general solution to the nonhomogeneous problem is their sum: y = yh + yp = C1 y1 + C2 y2 + yp Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). first order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). 3. The general solution to the nonhomogeneous problem is their sum: y = yh + yp = C1 y1 + C2 y2 + yp Solutions to nonhomogeneous differential equations • To solve a nonhomogeneous differential equation: 1. Find the general solution to the associated homogeneous problem, yh(t). first order DE second order DE 2. Find a particular solution to the nonhomogeneous problem, yp(t). 3. The general solution to the nonhomogeneous problem is their sum: y = yh + yp = C1 y1 + C2 y2 + yp • For step 2, try “Method of undetermined coefficients”... Method of undetermined coefficients (3.5) Method of undetermined coefficients (3.5) • Example 4. Define the operator general solution to L[y ] = e 2t L[y ] = y + 2y − 3y. ￿￿ . That is, ￿ Find the y ￿￿ + 2y ￿ − 3y = e2t . Method of undetermined coef...
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This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at The University of British Columbia.

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