Find the real-valued general solution and circle it. Then draw a phase portrait. Clearly label the two eigenvectors and sketch several other trajectories using arrows to indicate their direction as t increases.

If a > 0, find the eigenvalues of x" + λax = 0, x (0) = x(b) = 0.

a) Write the initial value problem in vector form. b) Solve by using eigenvalues/eigenvectors. c) Write the solution in x(t), y(t) form.

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determine eigenvalues and eigenvectors if the eigenvalues are real. Also, determine the general solution of the following linear systems of differential equations:dx/dt = ax + by,dy/dt = cx + dy.

Please answer this question asap I will rate you for sure. Determine the dominant eigenvector of each of the following matrices: ˆ ( 0.45 0.85) (0.55 0.15 )

Please solve this question in hand writting. Again please need it in hand writting.