Find all the equilibrium solutions of the system of differential equations dx/dt = gz - hx, dy/dt = c/a + bx, dz/dt = ey - fz. Determine the stability or instability of these solutions if any of the values g, e, or c equals zero.
Added by Raul W.
Step 1
Equilibrium solutions occur when dx/dt, dy/dt, and dz/dt are all equal to zero. Setting dx/dt = 0, we get gz - hx = 0. Solving for z, we get z = hx/g. Setting dy/dt = 0, we get c/a + bx = 0. Solving for x, we get x = -c/(ab). Setting dz/dt = 0, we get ey - fz Show more…
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