- #1
matematikawan
- 338
- 0
I think I know how to solve
[tex]\frac{d\vec{x}}{dt}= A \vec{x}[/tex]
where A is a constant nXn matrix. We just compute the eigenvalues and the corresponding eigenvectors.
But how do we solve
[tex]\frac{d^2\vec{x}}{dt^2}= A \vec{x}[/tex]
Can we say straight away that the solution is (following that of one dependent variable)
[tex]\vec{x}(t) = exp(-Mt) \vec{x}_1+ exp(Mt) \vec{x}_2 [/tex]
where M2=A and x1 and x2 are constant vectors.
[tex]\frac{d\vec{x}}{dt}= A \vec{x}[/tex]
where A is a constant nXn matrix. We just compute the eigenvalues and the corresponding eigenvectors.
But how do we solve
[tex]\frac{d^2\vec{x}}{dt^2}= A \vec{x}[/tex]
Can we say straight away that the solution is (following that of one dependent variable)
[tex]\vec{x}(t) = exp(-Mt) \vec{x}_1+ exp(Mt) \vec{x}_2 [/tex]
where M2=A and x1 and x2 are constant vectors.