# Homework Help: Laplace transorm problem

1. May 3, 2012

### eddiej90

1. The problem statement, all variables and given/known data
Using the laplace transform technique, solve the ordinary differential equation:
d2y/dt2+4.2dy/dt+4.5y=0 initial conditions: y(0)=1 and y'(0)=1

2. Relevant equations
From laplace tables:
d2y/dt2=s2Y-sy(0)-y'(0)
dy/dt=sY-y(0)

3. The attempt at a solution
After using the laplace tables to convert the equation, and rearranging it to make Y the subject, I have come to this point:
Y=(s+5.2)/s2+4.2s+4.5
Iv tried completing the square on the denominator and other methods but cannot get to a point that looks similar to the laplace tables in order to convert it back. Im pretty sure i need to use the ones under the section "General approach to quadratic functions of the form as2 + bs + c" however i have completely no idea as to what to do with α and β

2. May 3, 2012

3. May 4, 2012

### eddiej90

Thamkyou for the link, however you cannot factorise the denominator, unless you complete the square. Can you use the partial fraction method with completing the square?

4. May 4, 2012

### sunjin09

Your denominator can certainly complete the square, s^2+4.2s+4.5=(s+2.1)^2-2.1^2+4.5, doesn't it? Obviously no need for partial fraction decomposition