Determine the stability or instability of all solutions of the following systems of differential equations
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Determine the stability or instability of all solutions of the following systems of differential equations ....
1. Find general solutions to the following differential systems of equations using dsolve: a. x' = y + t, y' = 2 -x+t b. x'=s-X, y' = -y - 3x, C. X" = x - x - y, y = -x- y - y - s', s" = -95 d. Solve the equations in c. above with the initial conditions x(0) = 1, x'(0) = 0, y(0) = -1, y'(0) = 0, $(0) = 1, s'(0) = 0, and plot...
DIFFERENTIAL EQUATIONS
Solutions of Systems of Linear Differential Equations
(L01.5 - 15 points) Show that the general solution of the nonhomogeneous linear system is x=(1 71}x+ []}<+[4.]e + 3' X=al_2-vzlevat +al-1 + vale-vēt + [1]{2+{2}]++ [4]
2. Differential equations and direction fields (a) Find the general solution to the differential equation y' = 20e3+ + + (b) Find the particular solution to the initial value problem y' = 64 – 102, y(0) = 11. (e) List the equilibrium solutions of the differential equation V = (y2 - 1) arctan() (d) List all equilibrium solutions of the differential equation, and classify the stability of each: V = y(y - 6)(n-10) (e) Use equilibrium solutions and stability analysis...
Determine all periodic solutions, all limit cycles, and determine their stability charac- teristics for the following system dr dt -1
Use the Method of Undetermined Coefficients to find all solutions of the differential equations = [100] [1] 2 1 -2 x+|0 ect, | 3 2 1 U c# 1.
3. Find the solutions to the following differential equations: [mark 25% d2x dx 5 2x 5 (1) dt2 dt x(0) (0) 0 (2) Use the Final Value Theorem to determine x(t) as t -» co from X(s) Note: Dots denote differentiation with respect to time
3. Find the solutions to the following differential equations: [mark 25% d2x dx 5 2x 5 (1) dt2 dt x(0) (0) 0 (2) Use the Final Value Theorem to determine x(t) as t -» co...
need help all those questions.
10. Solve the following systems of linear differential equations: 11. Determine the Laplace transform of each of the following functions: (a) fe)-2t+1, 0StcI , 21 (b) f(t) te (c) f(t) = cos t cos 2t (Hint: Examine cos(a ± b).) Determine the inverse Laplace transform of each function: 12. (a) F(s) = 52 +9 is Demin 13. Determine L{kt cos kt + sin kt). 0, t< a 14. Determine L(cos 2t)U(t-r), where U(t-a)={ 15. Use...
Find all equilibrium solutions of the system of ordinary
differential equations d
(6 points) Find all equilibrium solutions of the system of ordinary differential equations ry - 2x dir dt dy dt = my - r - 2y + 2,
this is from differential equations ch8 section 2 please write
clearly and show all steps. thanks!
Use the methods of section 8.3 to find the general solutions of the given systems of differential equations in the following two problems. 4. = X-1 dx dt dy dt = -x + 2y
this is from differential equations ch8 section 2. please write
clearly and show all steps
Use the methods of section 8.2 to find the general solutions of the given systems of differential equations in the following three problems. 2. dx dt 2x + y dy = -x + 4y dt