EtherNohow
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Let x(t)=
[x1(t)
x2(t)]
be a solution to the system of differential equations:
x′1(t)=−2x1(t)+2x2(t)
x′2(t)==−6x1(t)+9x2(t)
If x(0)=
[4
-2]
find x(t).
I got the eigenvalues to be -6 and -5, but I don't know how to calculate the coefficients in front of the exponents. For lambda=-6 I get the vector (1, -2) and for lambda=-5 I get the vector (2, -3). I think these would be the coefficients, but I'm not sure, and I don't know how to use the initial values for x(0). Thanks for your help!
[x1(t)
x2(t)]
be a solution to the system of differential equations:
x′1(t)=−2x1(t)+2x2(t)
x′2(t)==−6x1(t)+9x2(t)
If x(0)=
[4
-2]
find x(t).
I got the eigenvalues to be -6 and -5, but I don't know how to calculate the coefficients in front of the exponents. For lambda=-6 I get the vector (1, -2) and for lambda=-5 I get the vector (2, -3). I think these would be the coefficients, but I'm not sure, and I don't know how to use the initial values for x(0). Thanks for your help!