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## Initial value problem using Laplace Transform

I have to solve the IVP: $$\begin{cases} y''+by'-cy=1\\ y(0)=y_0\\ y'(0)=y'_0 \end{cases}$$

Suppose $$Y(s)=\frac{s^2+2s+1}{s^3+3s^2+2s}$$

We have to find $b,c,y_0$ and $y'_0$

I have found that: $$(s^2+s+1)Y(s)-(s+1)y_0-y'_0=1/s$$

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## Solve the initial value problem using Laplace transforms. y"+y=f(t) , y(0)=0 , y'(0)=1

## Answered question

## Answer & Explanation

Skilled 2021-09-07 Added 109 answers

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## Browse Course Material

Course info, instructors.

- Prof. Arthur Mattuck
- Prof. Haynes Miller
- Dr. Jeremy Orloff
- Dr. John Lewis

## Departments

- Mathematics

## As Taught In

- Mathematics Differential Equations Linear Algebra

## Learning Resource Types

Differential equations, laplace transform: solving initial value problems.

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## Session Overview

Session activities.

Read the course notes:

- Laplace Transform: Solving Initial Value Problems: Introduction (PDF)
- Laplace Transform Table (PDF)
- Table Entries: Derivative Rules (PDF)
- Precise Definition of Laplace Inverse (PDF)
- Laplace: Solving Initial Value Problems (PDF)
- IVP’s and t-translation (PDF)
- IVP’s: Longer Examples (PDF)

Watch the problem solving video:

- Laplace: Solving ODE’s

Complete the practice problems:

- Practice Problems 29 (PDF)
- Practice Problems 29 Solutions (PDF)

## Check Yourself

Complete the problem sets:

Problem Set Part I Problems (PDF)

Problem Set Part I Solutions (PDF)

Problem Set Part II Problems (PDF)

Problem Set Part II Solutions (PDF)

## VIDEO

## COMMENTS

We have to find b,c,y₀ and y'₀. I have found that:(s^2+s+1)*Y(s)-(s+1)y₀-y'₀=1/s. How do I proceed further

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Find step-by-step Engineering solutions and the answer to the textbook question Use the Laplace transform to solve the initial value problem. y' – 2y = 1 – t; y(0) = 4

This section provides materials for a session on operations on the simple relation between the Laplace transform of a function and the Laplace transform of its derivative

To solve the initial value problem using Laplace transforms, we first take the Laplace transform of both sides of the given equations. Using the property of the Laplace transform for derivatives, we have

This section provides materials for a session on operations on the simple relation between the Laplace transform of a function and the Laplace transform of its derivative