- #1
Saladsamurai
- 3,020
- 7
!Solving a Differential Eq using Laplace and Unit-Step function
I am having a terrible time just starting this. I need some explanation here. I have given up on the text I am using...
I need to solve the following piecewise function using Laplace and Unit-Step function:
y"+4y=f(t) y(0)=-1, y'(0)=0
where f(t)= t, t<2
5, t>2
Now I condensed it to one line using the Unit Step function giving:
[itex]y''+4y=t-t*U(t-2)+5*U(t-2)[/itex]
Applying Laplace to the LHS is easy enough, but what is the Laplace of the unit step function? I am having a hard tome extrapolating it from the text.
So far I have
[itex]s^2Y(s)-sy(0)-y'(0)+4Y(s)=\frac{1}{s^2}-?[/itex]
Could somebody help me out with the "U" terms here?
Thank you
Homework Statement
I am having a terrible time just starting this. I need some explanation here. I have given up on the text I am using...
I need to solve the following piecewise function using Laplace and Unit-Step function:
y"+4y=f(t) y(0)=-1, y'(0)=0
where f(t)= t, t<2
5, t>2
The Attempt at a Solution
Now I condensed it to one line using the Unit Step function giving:
[itex]y''+4y=t-t*U(t-2)+5*U(t-2)[/itex]
Applying Laplace to the LHS is easy enough, but what is the Laplace of the unit step function? I am having a hard tome extrapolating it from the text.
So far I have
[itex]s^2Y(s)-sy(0)-y'(0)+4Y(s)=\frac{1}{s^2}-?[/itex]
Could somebody help me out with the "U" terms here?
Thank you