Solve the system of first-order linear differential equations. (Use C1 and C2 as constants.) y1' = y1 y2' = 4y2 (y1(t), y2(t)) = ( )
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We can solve it by assuming a solution of the form $Y_2(t) = e^{rt}$: $$ r^2 e^{rt} = 4e^{rt} $$ Dividing both sides by $e^{rt}$, we get: $$ r^2 = 4 $$ This equation has two solutions: $r = 2$ and $r = -2$. Show more…
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