in the second problem, e is raised to the power -t
i am stuck on these two problems. i can apply laplace tranforms and then i cant figure out how to solve for the inverse to finish the problem.
1) X” -4X = 3t ; X(0) = 0 ; X’(0) =0
1)X” + 4X’ +13X = te-t ; X(0)= 0 ; X’(0) = 2
please help!!
Applying the Laplace Transform, we see that
Now, applying the initial equations, we are left with
Solving for , we have
Take note that
So, we have
Taking the inverse Laplace Transform, we have
Does this make sense?
For this one, its somewhat similar to the first one. I'll get you started:1)X” + 4X’ +13X = te-t ; X(0)= 0 ; X’(0) = 2
please help!!
Apply the Laplace Transform to both sides, you should have
Applying the initial conditions, we're left with
Solving for , we have
Can you try to find the inverse Laplace transform on your own? For the first term, apply partial fractions. On the second, my hint to you is (hinting at the fact that a translation is required)