Resolver y'' - 4y' + 3y = 1 con Transformada de Laplace paso a paso

Published on November 9, 2026

Calculus

Solución paso a paso de la ecuación diferencial lineal de segundo orden y'' - 4y' + 3y = 1 con condiciones iniciales y(0)=1 e y'(0)=4, usando transformadas de Laplace y fracciones parciales para obtener y(t) = 1/3 - e^t + (5/3)e^(3t).

Question

Resuelve Paso a Paso: y'' - 4y' + 3y = 1, y(0) = 1 , y'(0) = 4. mediante transformadas de Laplace

Answer

Paso 1: Transformar la ecuación. Aplicando

y usando

Paso 2: Despejar . Agrupando términos en

y constantes:

Paso 3: Descomposición en fracciones parciales.

Paso 4: Transformada inversa.

Verificación rápida:

✓,

✓.

Respuesta final:

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features

Related math solutions

Solving Limits and Continuity Problems Graphically and Algebraically

Learn how to solve limit problems using function graphs and algebraic substitution, covering direct substitution and indeterminate forms.

Limit of ln((1+1/x)^(2x)) as x approaches infinity

Calculate the limit of the natural logarithm of (1+1/x) raised to the power of 2x as x approaches infinity, using logarithm properties and known limits or L'Hopital's rule.

Solving Second Order Linear Differential Equations in Economics

Learn how to solve a first-order linear differential equation derived from a beef market model to analyze price dynamics and market stability.

Inverse Laplace Transform Practice Problems and Step-by-Step Solutions

This set of exercises focuses on finding the inverse Laplace transforms of various rational and exponential functions, including the use of partial fraction decomposition and shifting theorems.

Evaluating the Integral of x^2 / ((x^4+x^2+1)(ax^2+1))

Learn how to evaluate the complex rational integral using partial fraction decomposition and algebraic substitution techniques.

🔎 Explore All Shared Math Solutions