Let x(t)=(adsbygoogle = window.adsbygoogle || []).push({});

[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!

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# I Question about using matrices for differential equations

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