Please walk me through these problems step by step.
1. Compute the Laplace transform of e^(-10t) = u(t).
2. Compute the inverse Laplace transform of:
X(s) = (3s^2+2s+1) / (s^3+5s^2+8s+4)
3. Use Laplace transforms to compute the solution to the differential equation given in the attachment.© BrainMass Inc. brainmass.com October 25, 2018, 4:08 am ad1c9bdddf
Differential Equation and Matrix Determinant
1.The ODE X"+ kX = 0 has different types solution depending on sign of k.
We consider the three possible cases separately.
k=0: X"=0 so that X(x)=Ao+Box, X'(0)=0 implies Bo=0 so that X(x)=Ao. Finally, X(1)=0 implies Ao=0 and there is only trivial solution X=0.
The matrix has determinant e^mu + e^-mu= 2cosh.mu, which is never zero and it follows that pair of equations has unique solution Ahat=Bhat=0 and only trivial solution X=0.