Writing for given system becomes
The same can be written as
Which is the standard form
Correct Option is 3rd one
- Question 2 1 point dy Suppose you have to solve the following system by elimination...
Suppose you have to solve the following system by elimination d²x dy j? y dy 9y+672 + + 8y = 82 + 5 sint dt2 dt dc + + 3х dt dt2 dt The standard form of the system is O (2D - 8)x+ (D+ 8)y = 5 sint (D - 3)2 + (2D+D+9)y= 6t2 (D2 – 8)x+ (D+8)y= 5 sint (D-3)x +(D2 +D+9)y+ 6+2 = 0 (D2 - 8)2 + (D+ 8)y - 5 sint = 0 (D –...
Question 1 : Solve the following system of equations: du at = 22 + +3y dy = 2x + y dt Question 2: State if the following system of equations have Unique solution, no solution or infinite solutions. Explain why? dx = x+2y at dy dt = x+2y
Problem # 1: (70 points) Solve the following problems (a) and (b) using Laplace Transform: a) (7 points) y(0)-y'(0)-0 y"(0)-1 b) (dX/d't) + 3 (dy/dt) + 3y-0 (7 points) (d'x/d't) +3y-te' x(0) = 0 x'(0) = 2 y(0) = 0 c) An nxn matrix A is said to be skew-symmetric if AT--A. If A is a 5x5 skew-symmetric matrix, show that 9detA)-0 (4 Points) d) Suppose A is a 5x5 matrix for which (detA) =-7, what is the value of...
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
QUESTION 2 Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the tetrahedron cut from the first octant by the plane yz + 9(1 -y/10)3(1 -x/9-y/10) a dz dy dx 0 0 0 10(1 -x/9) ,3(1-x/9-y/10) 9 dz dy dx 0 0 1-x/9-y/10 C.9 1 -y/10 dz dy dx 0 0 0 d. 9 1 -x/9 1-x/9-y/10 dz dy dx 0 0 0
Solve the given system of differential equations by systematic elimination. = -x + 2 dx dt dy = -y + z dt dz = -x + y dt
For the system described by the following differential equation d3y(t) d2y(t) d2x(t) dy(t) 3 dt dx(t) 9 dt y(t) 5x(t) 7 2 6 dt3 dt2 dt2 Express the system transfer function using the pole-zero plot technique a) b) What can be said about the stability of this stem? For the system described by the following differential equation d3y(t) d2y(t) d2x(t) dy(t) 3 dt dx(t) 9 dt y(t) 5x(t) 7 2 6 dt3 dt2 dt2 Express the system transfer function using...
In Problems 3-6, find the critical point set for the given system. dx 4. dx = x-y, 3. dt y1 dt dy dy = x2 y2 - 1 dt = x + y + 5 dt dx dx x2- 2xy y2- 3y 2 6. 5. dt dt dy dy 3xy - y2 (x- 1)(y 2) dt dt
Solve the following differential equation using variation of parameters. d yt) 2 dy() +7- + 10y() u(t) dt dt2 y(0) 0, y'(0) = 3 d yt) 2 dy() +7- + 10y() u(t) dt dt2 y(0) 0, y'(0) = 3
#10 all parts In each of Problems 5 through 18: (a) Determine all critical points of the given system of equations. (b) Find the corresponding linear system near each critical point. (c) Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system? (d) Draw a phase portrait of the nonlinear system to confirm your conclusions or to extend them in those cases where the linear system does not provide definite information about the...