Quiz 3 Study Guide

Quiz 3 Study Guide - Make sure that the function g(t)...

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Quiz 3 Study Guide 1. Given the following differential equation: a. Verify that y 1 and y 2 are solutions b. Find W[y 1 , y 2 ] Calculate the first and second derivatives of the initial y 1 and y 2 conditions then substitute the given values into the differential equation. Solve to find the Wronskian determinant.
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2. Given the following 2 nd order homogenous differential equation: a. Find two linear independent solutions b. Solve with initial value conditions Find the characteristic function and solve for the roots . Roots Characteristic Function, y Solve using the initial value conditions to find C 1 and C 2 .
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3. Given the following 2 nd order non-homogenous differential equation: a. Find two linear independent solutions b. Solve with initial value conditions Method of Undetermined Coefficients Find the characteristic function and solve for the roots . Use the table above to find the corresponding function y.
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Unformatted text preview: Make sure that the function g(t) belongs to the class of either exponential functions, sines, cosines, or polynomials Assume a particular solution for Y i (t) consisting of the appropriate function. If there is any duplication in Y i (t) with the solutions of the homogenous equation, multiply Y i (t) by t. Form the sum of the general solution of the homogenous equation and the particular solution of the non-homogenous equation. Use the initial conditions to determine the values of the arbitrary constants remaining in the general solution. 4. Use Laplace transform to solve the following 2 nd order homogenous differential equation. Break up the equation to take the Laplace transform of each component, . Use using the coefficients of the original differential equation. Once simplified, solve for Y(s). Set...
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This note was uploaded on 09/12/2011 for the course MATH 2403 taught by Professor Wang during the Fall '07 term at Georgia Tech.

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Quiz 3 Study Guide - Make sure that the function g(t)...

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