- #1

- 58

- 0

Find the general solution to the following differential equation:

[1 -12 -14]

x'= [1 2 -3]*x

[1 1 -2]

the eigeinvalues that I found are 1 , +5i, -5i

the general solution that I found is

c1e^e[25] + c2[cos5t+5sin5t] + c2[-5cos5t+sin5t] + c3[2] + c3t[1-5i]

[-7] [cos5t ] [sin5t ] [2] [1 ]

[6 ] [cos5t ] [sin5t ] [1] [1 ]

Am I suppose to have imaginary values in my solution?

I'm supposed to find the solution if x(0)=2i-5j+3k

I just plug 0 in for all the t's and solve for the constants which is no problem for me. The problem that I'm having is the fact that I have an imaginary value in the solution.

I'm also suppose to find the phase portrait.