Systems of Ordinary Differential Equations (original) (raw)

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2. Linear Systems of Three or More Ordinary Differential Equations;x = x(t), y = y(t), z = z(t)

1. _x_′ = ax, _y_′ = bx + cy, _z_′ = dx + ky + pz.
2. _x_′ = cy − bz, _y_′ = az − cx, _z_′ = bx − ay.
3. _ax_′ = bc(y − z), _by_′ = ac(z − x), _cz_′ = ab(x − y).
4. _x_′ = (a_1_f + g)x + a_2_fy + a_3_fz, _y_′ = b_1_fx + (b_2_f + g)y + b_3_fz, _z_′ = c_1_fx + c_2_fy + (c_3_f + g)z.
5. _x_′ = h(t)y − g(t)z, _y_′ = f(t)z − h(t)x, _z_′ = g(t)x − f(t)y.
6. x_′_k =a _k_1_x_1 +a _k_2_x_2 + … +aknxn; k = 1, 2, …, n.

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