Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Solve by variation of parameters

**Equation 21:** \[ y'' - 2y' + 5y = e^x \cos(2x) \] This is a second-order linear differential equation with constant coefficients and an exponential trigonometric forcing function. The left-hand side represents a homogeneous linear differential equation, while the right-hand side represents the non-homogeneous part, involving the product of an exponential function and a trigonometric function. Solving this type of equation typically involves finding the complementary (homogeneous) solution and particular (non-homogeneous) solution.
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Transcribed Image Text:**Equation 21:** \[ y'' - 2y' + 5y = e^x \cos(2x) \] This is a second-order linear differential equation with constant coefficients and an exponential trigonometric forcing function. The left-hand side represents a homogeneous linear differential equation, while the right-hand side represents the non-homogeneous part, involving the product of an exponential function and a trigonometric function. Solving this type of equation typically involves finding the complementary (homogeneous) solution and particular (non-homogeneous) solution.
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