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So in my notes it says that the general solution to a system of linear equations:

x_{1}'(t) = a_{11}x_{1}(t) + a_{12}x_{2}(t)

x_{2}'(t) = a_{21}x_{1}(t) + a_{22}x_{2}(t)

is:

x(t) = c_{1}e^{λ1t}v_{1}+ c_{2}e^{λ2t}v_{2}

What I don't understand is how you go from the system of equations to the general solution, the notes did not explain how. This was for my linear algebra class and I have never taken a differential equation class. However I am familiar with calculus so could someone please explain this?

I know how to solve the general solution, just not sure how it was derived.

Thanks!

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# Homework Help: Confused about system of linear differential equations?

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