Resolver y'' + 2y' + 5y = 0 con condiciones iniciales usando transformada de Laplace

Published on November 9, 2026

Calculus

Solución paso a paso de la ecuación diferencial lineal de segundo orden y'' + 2y' + 5y = 0 con y(0) = y'(0) = 1 mediante transformadas de Laplace, completando el cuadrado y antitransformando a una solución oscilatoria amortiguada.

Question

Resuelve paso a paso: y'' + 2y' + 5y = 0, y(0) = y'(0) = 1 , mediante transformadas de Laplace

Answer

Paso 1: Transformar la ecuación

Aplicando

Paso 2: Despejar

Paso 3: Completar el cuadrado en el denominador

Reescribiendo el numerador en términos de

, por lo que

Paso 4: Antitransformar

Usando

Respuesta final:

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