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WindowTitle->18. ODEs with Constant Coefficients | Laplace Transforms in \
Theory and Practice
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In this chapter, one of the main applications of the Laplace transform will \
be discussed: solutions of linear ordinary differential equations (ODEs). The \
Laplace transform method is handy for differential equations with initial and \
boundary conditions. It is also useful for solving systems of ODEs. \
Applications to mechanical and electrical systems will be addressed in the \
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Suppose that you are given the following second-order differential equation:\
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To do so, first apply the Laplace transform to the previous equation. Since \
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linearity property and the derivative theorem will be used to simplify the \
left-hand side. It helps to reduce the Laplace transform of the derivatives \
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The Laplace transform method proves to be useful also for the boundary value \
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The Laplace transform is an excellent tool to solve ODEs with constant \
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Applying the Laplace transform on this equation and using the derivative \
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This answer agrees with the solution obtained in the first approach. \
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Applying the Laplace transform on the differential equation, one obtains:\
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Apply the inverse Laplace transform to return to the time domain:\
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