Рет қаралды 69,572
▼ IMPORTANT ▼ In this video we will see a solved example (solved exercise) of a non-homogeneous second-order linear differential equation of constant coefficients, solved by the Laplace transform method, with initial conditions and a function defined in pieces. We first write the function as a combination of unit step functions (translated Heaviside function) and use the second translation theorem to compute the Laplace transform. We transform the equation, compute the Laplace transform of the second derivative of “y”, solve for the transform, separate into partial fractions (simple fractions), and compute the term-by-term inverse using the formulas for sine, cosine, constant, and polynomials. , and also using second translation theorem for inverses. Everything step by step.
#EDO # Differential Equations #Laplace
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Laplace Transforms: • Transformadas de Laplace
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** BIBLIOGRAPHY **
- Differential Equations, Edwards and Penney
- Differential Equations, Daniel A. Marcus
- Differential Equations, Dennis G. Zill
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