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I have the following initial value problem:

\[ x' = x + 2y + 3z \]

\[ y' = 4y + 5z \]

\[ z' = 6z \]

All I'm looking to do is find the general solution to this system, and as long as I'm doing this correctly I have these answers:

\[ y(t) = K_2e^{4t} + \tfrac{5K_1}{2}e^{6t} \]

\[ z(t)=K_1e^{6t} \]

But I'm having trouble getting x(t) to finish this up. Any help on what my next steps should be?