Please find general solution and find the type and stability of critical point (0,0)
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Please find general solution and find the type and stability of critical point (0,0) x ]'...
Find the general solution of the following system and determine the type and stability of critical point (0,0) [= [": 3] |
(1 point) Find the general solution of the differential equation on (0,0): xy" + xy + (576x2 – 484)y=0 General solution: y=c] ( )+czy ( ) NOTE REGARDING ANSWER ENTRY: To enter a Bessel function of the form J. (b), you should type a in the first blank and bx in the second blank. Subscripts should be listed in decreasing order, if applicable.
2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates. 2. (2 pts) Determine the type of the critical point (0,0) for the system x' =-7x+ 5y, y' =-6x 4y. Sketch a phase portrait based on the eigenvectors, and the direction that the sign of the eigenvalue indicates.
7. Find and classify the type and stability of the critical point for each system below x' =-2x1-3x2 + 8 xz'= 3x1 + 2x2-8 Where α is a real number.
1. Classify the stability type of the equilibrium point (0,0) of the following linear planar homogeneous systems (same notation as in the previous homework). -(G3) 1 -3 2 -1 A-(25 4 -5
Consider the nonlinear system ?x′ = ln(y^2 − x) and y'=x-y-1 (a)Find all the critical points (b)Find the corresponding linearized system near the critical points. (c) Classify the (i) type (node, saddle point, · · · ), and (ii) stability of the critical points for the corresponding linearized system. (d) What conclusion can you obtain for the type and stability of the critical points for the original nonlinear system?
(1 point) Classify the critical point (0,0) of the linear 2 x 2 system by computing the trace T, the determinant A and the discriminant D=72 – 4A. xt' = -5x + 3y, y' = 2x – 7y.
Help Entering Answers 9cy (1 point) Find all the critical points of f(x,y) = 2x3 +y* Σ (0,0),(3(2)(2/3))/2, (3(2)^(1/3))/2) List separate answers with a comma. Help Entering Answers 9cy (1 point) Find all the critical points of f(x,y) = 2x3 +y* Σ (0,0),(3(2)(2/3))/2, (3(2)^(1/3))/2) List separate answers with a comma.
3. (2 points) Determine the stability and the type of the critical point(s) of the following system of differential equations 1-441-yi
Consider the system of differential equations Classify the critical point (0,0) as to type and determine whether it is stable, asymptotically stable, or unstable draw several (at least eight) trajectories in the xy-plane. 5 0 -5 5 0 -5