Exact Solutions > Systems of Ordinary Differential Equations > Linear Systems of Three or More Ordinary Differential Equations

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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′ = (a₁f + g)x + a₂fy + a₃fz,   y′ = b₁fx + (b₂f + g)y + b₃fz,   z′ = c₁fx + c₂fy + (c₃f + 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_k1x₁ + a_k2x₂ + … + a_knx_n;   k = 1, 2, …, n.