Laplace transform applied to a differential equation

  • #1
131
22

Homework Statement


Solve ##\frac{dy}{dt} -y = 1, y(0) = 0## using the laplace transform

Homework Equations




The Attempt at a Solution


##\mathcal{L}\big\{\frac{dy}{dt}\big\} - \mathcal{L}\big\{y\big\} = \mathcal{L}\big\{1\big\}##

##sY(s) - y(0) - \frac{1}{s^2} = \frac{1}{s}##

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

Applying the inverse Laplace leads to:

##y(t) = \frac{1}{2}t^2 + t##

Which is nothing like the answer obtained with separation of variables. What have I done wrong here?
 

Answers and Replies

  • #2
131
22
Okay, I see the trouble. Made an error with ##\mathcal{L}\big\{y\big\}##. Problem solved
 

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