Hello, boys .
In my home work is to solve these 3 equations , and a textual problem , but the second day I can not solve them. My professor said that these tasks are very easy, I just need to better analyze, but I think he has a good sense of humor.
1. Find a nontrivial solution of differential equation .
2. Solve the differential equation .
3. Using Laplace transform, solve the differential equation if and .
Please help me.
3. Using Laplace transform, solve the differential equation if and .
So, we have
Next we will use the third decomposition theorem. In this case we can use this theorem, because and uniformly on the entire plane except for poles.
The function has poles .
Next we will find residues of the function in these poles.
Similarly, .
Sum these of two residues
3. We will find a residue in the point
if
if
if
Sum of these two residues
Finally, we have