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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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