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# MATH 411 HOMEWORK 3 1. For the following equations, Find the general real-valued solution. Classify the equilibrium at the origin. Sketch a phase...

Can you do the first problem in the attach file.

MATH 411 HOMEWORK 3 1. For the following equations, Find the general real-valued solution. Classify the equilibrium at the origin. Sketch a phase plane diagram. (a) x 0 = ± 2 2 2 - 1 ² x (b) x 0 = ± 1 1 - 1 1 ² x (c) x 0 = ± 0 9 - 9 0 ² x 2. Find the general solution to x 0 = 3 0 4 0 2 0 0 0 - 3 x 3. Solve the initial value problem x 0 = ± 1 3 3 1 ² x, x (0) = ± - 2 1 ² 4. Find the general solution (using either of the methods we discussed in class) for x 0 = ± 2 1 - 9 - 4 ² x 5. Find e At for each of the following matrices: (a) 2 - 2 2 0 1 1 - 4 8 3 (eigenvalues are 1, 2, and 3) (b) 1 1 0 0 1 0 0 1 1 (you can do this without using the Putzer algorithm) 1 Sign up to view the entire interaction

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fetlee! See how laborious is your work. Still I... View the full answer 1a) the Eigen values and the respective Eigen vectors of are 3, -2 and
So, the solution of the system of differential equations is
Writing the differential equations, we see that
Equating the right...

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