Laplace Transform Prob: y"-2y'-3y=1 if y(0)=0, y'(0)=1

RobCherry

New member
Joined
Aug 15, 2007
Messages
6
Solve the Initial Value problem using Laplace Transforms:

y" - 2y' - 3y =1 if y(0)=0, and y'(0)=1
 
I go ahead and throw a bone on one of these.

\(\displaystyle \L\\y''-2y'-3y=1, \;\ y(0)=0, \;\ y'(0)=1\)

\(\displaystyle \L\\y''=p^{2}Y-py(0)-y'(0)\)

\(\displaystyle \L\\y'=pY-y(0)\)

\(\displaystyle \L\\p^{2}Y-py(0)-y'(0)-2(pY-y(0))-3Y=\frac{1}{p}\)

Now, solve for y, perform partial fractions on the right side and look up the inverse LaPlace in a table.

Can you see all of the lines?. Two are not displyaying correctly.
 
Top