Math 216 Homework webHW4 Problem 5 Consider the system from

Math 216 Homework webHW4, Problem 5 Consider the system from the previous problem, X. -1 7 You verified there that the vectors 3e4t 6t and x2= -1eAt are solutions to this system. Use these to find a particular solution satisfying the initial condition x(0) =

Solution

Clearly here ....
The first solution is
x1 = -3e^(4t) + e^(6t) + C

Using the initial condition x(0) = 3,
3 = -3 + 1 + C
C = 5

So, -3e^(4t) + e^(6t) + 5 ----> first answer

Now, second solution is :
x2 = -e^(4t) + e^(6t) + K

Using initial condition x(0) = 5 :
5 = -1 + 1 + K
K = 5

So, we have
x2 = -e^(4t) + e^(6t) + K

x2 = -e^(4t) + e^(6t) + 5 --> second ans

So, xp is :
-3e^(4t) + e^(6t) + 5 --> first blank
-e^(4t) + e^(6t) + 5 --> second blank