Find the solutions for the scalar ODEs (with a constant) dx = ax, dt (ii) ਕੰਮ =-y. Now, consider the linear system of OD

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Find the solutions for the scalar ODEs (with a constant) dx = ax, dt (ii) ਕੰਮ =-y. Now, consider the linear system of ODES dx = ax dt dy -y dt = (a) Find the general solution of the system. (b) Sketch the phase portrait of the system for (i) a = -1, (ii) a = 0, and (iii) a = 1. Include the direction of the eigenvectors and sample trajectories. (c) Assume that where a < -1. Show that all trajectories become parallel to the y-direction as t → 00, and parallel to the x-direction as t →-00. (Hint: Examine the slope dy/dx.)