Sketch the phase portrait of
y'' - 3y' + 6y = 0 on the plane (y; y0)
9-Sketch the phase plane portrait (phase portrait) for the given system of differential equations. Include all your calculations (phase portrait without proper calculations wont be accepted). (5 Points) X' - x + 3y ly - 2x - 4y
1) Find the general solution of di = Ay where Then sketch the phase portrait in the x-y plane, where Finally, classify the equilibrium solution at the origin as a source, spiral sink, etc. 2) Repeat for the matrix | 3 -31 -2 -2] 3) Repeat for the matrix 4 — 4) Repeat for the matrix [95 -9 15 but you don't need to sketch the phase portrait.
Classify the critical point (0, 0) of the given linear system. Draw a phase portrait. dx/df 3x+ y a. dx/dt -x+ 2y dx/dt =-x +3y dy/dt -2x + y dy/dt x+ y Classify the stationary point (0, 0) of the given linear system. Draw a phase portrait. dy/dt -x+y b. dx/dt =-2x-y dx/dt-2x +5/7 y dx/dt 3x-y dx/dt 3x dy/dt 3x- y dy/dt 7x- 3y dy/dt x+y dy/dt 3y
Sketch the phase portrait for each linear system below
Y. dt - (33) = (211) dY dt Y.
For each of the linear systems below a. Sketch the phase portrait by hand
For each of the linear systems below a. Sketch the phase portrait by hand
Differential Equation Roots rı, 12 General Solution y" - 6y' + 3y = 0 y" + 2y + 5y = 0 Y" +22y + 121y = 0
Find the solution of the differential equation 6y-1 ly, +3y = 0
Find the solution of the differential equation 6y-1 ly, +3y = 0
Solve Utilizing Laplace Transformations: 3y" + 3y' + 6y = 3e^(-t) * sin2t with initial conditions y(0) = 1 and y'(0) = -1
consider the initial value problem. y"+5/6y=1-1/5t , y(0)=Y0
Classify stability (i.e sync/source, spiral, saddle, center...) and sketch the phase portrait of the system ()-() 1 (а) А — -4 3 (2) ( -1 1 (b) А — -1 2 (с) А — 1 3
Classify stability (i.e sync/source, spiral, saddle, center...) and sketch the phase portrait of the system ()-() 1 (а) А — -4 3 (2) ( -1 1 (b) А — -1 2 (с) А — 1 3