Question

Solve the system: x' = (2 4 -1 6)x

Answer 1

`x=e^(8t)+c`

Explanation:

we have given x'=(24-16)x=8x

x' denotes the differenation

`(dx)/(dt)=8x` differentiation is performed with respect to t

by variable separable method we can write

`(dx)/(x)=8dt`

on integrating both side

`lnx=8t+c`

`x=e^(8t)+c` (property of log )

so the solution for x will be
`x=e^(8t)+c`