Consider the initial value problem dx dt dy dt =-y x(0) = m, y(0) = n....

 

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Consider the initial value problem dx dt dy dt =-y x(0) = m, y(0) = n. 1. Draw a direction field for the system. 2. Determine the type of the equilibrium point at the origin. 3. Use dsolve to solve the IVP in terms of m and n 4. Find all straight-line solutions 5. Plot the straight-line solutions together with the solutions with initial conditions (m, n) = (2, 1), (1,-2).(-2, 2), (-2,0) Consider the initial value problem dx dt dy dt =-y x(0) = m, y(0) = n. 1. Draw a direction field for the system. 2. Determine the type of the equilibrium point at the origin. 3. Use dsolve to solve the IVP in terms of m and n 4. Find all straight-line solutions 5. Plot the straight-line solutions together with the solutions with initial conditions (m, n) = (2, 1), (1,-2).(-2, 2), (-2,0)