(a) Find the solution to dy: dt dyz Y1 + 3y2 3y1 – V2 dt with the initial condition y1 (0) = 3, y2(0) = 0. Sketch this solution on a phase diagram.

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Chapter2: Second-order Linear Odes
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4. (a) Find the solution to
dyi
= 3y1 – 42
dt
dyz
= y1 + 3y2
dt
with the initial condition y1 (0) = 3, y2(0) = 0. Sketch this solution on a phase diagram.
(b) Find the general solution for the system
i = 9x – 7y + 3z
ý = 12x – 10y + 3z
ż = 16z – 16y + z.
In addition, find the single equilibrium solution for this system. How wo
stability of this point?
you characterise the
Transcribed Image Text:4. (a) Find the solution to dyi = 3y1 – 42 dt dyz = y1 + 3y2 dt with the initial condition y1 (0) = 3, y2(0) = 0. Sketch this solution on a phase diagram. (b) Find the general solution for the system i = 9x – 7y + 3z ý = 12x – 10y + 3z ż = 16z – 16y + z. In addition, find the single equilibrium solution for this system. How wo stability of this point? you characterise the
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