I'm stuck on this problem that involves drawing a phase portrait but I'm at a stand still.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Matrices and general solutions

**Physics Forums | Science Articles, Homework Help, Discussion**