Question

construct a Lyapunov function to show the zero solution of x' = -x + y -...

construct a Lyapunov function to show the zero solution of
x' = -x + y - x(x^2 + y^2)
y' = -2y + y(x^2 + y^2)

is asymptotically stable.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
y''+2y'-15y=0 Find the general solution determine from its roots if it is asymptotically stable, stable or...
y''+2y'-15y=0 Find the general solution determine from its roots if it is asymptotically stable, stable or unstable, and classify its type
Verify that the function y=x^2+c/x^2 is a solution of the differential equation xy′+2y=4x^2, (x>0). b) Find...
Verify that the function y=x^2+c/x^2 is a solution of the differential equation xy′+2y=4x^2, (x>0). b) Find the value of c for which the solution satisfies the initial condition y(4)=3. c=
Find the general solution. Express the solution in vector form. x' = x + 2y y'...
Find the general solution. Express the solution in vector form. x' = x + 2y y' = 4x+3y Find the general solution. Express the solution in scalar form. x' = −4x + 2y y' = − 5/2 x + 2y
Prove that the function f(x) = |x| is not differentiable at zero, and show that the...
Prove that the function f(x) = |x| is not differentiable at zero, and show that the function g(x) = |x|*x is differentiable at zero.
Let y be the solution of the equation a) y ′ = 2 x y, satisfying...
Let y be the solution of the equation a) y ′ = 2 x y, satisfying the condition y ( 0 ) = 1. Find the value of the function f ( x ) = ln ⁡ ( y ( x ) ) at the point x = 2. b) Let y be the solution of the equation y ′ = sqrt(1 − y^2) satisfying the condition  y ( 0 ) = 0. Find the value of the function  f ( x...
Show that the function f(z) =x^3-3xy^2+i((3x^2y-y^3) is differentiable
Show that the function f(z) =x^3-3xy^2+i((3x^2y-y^3) is differentiable
The real part of a f (z) complex function is given as (x,y)=y^3-3x^2y. Show the harmonic...
The real part of a f (z) complex function is given as (x,y)=y^3-3x^2y. Show the harmonic function u(x,y) and find the expressions v(x,y) and f(z). Calculate f'(1+2i) and write x+iy algebraically.
Show that f(x) = C1e4x + C2e-2x is a solution to the differential equation: y’’ –...
Show that f(x) = C1e4x + C2e-2x is a solution to the differential equation: y’’ – 2y’ – 8y = 0, for all constants C1 and C2. Then find values for C1 and C2 such that y(0) = 1 and y’(0) = 0.
Verify that the indicated function is a solution of the given differentialequation.x2y′′−xy′+ 2y= 0;y=xcos (lnx), x...
Verify that the indicated function is a solution of the given differentialequation.x2y′′−xy′+ 2y= 0;y=xcos (lnx), x >0
Solve the DE: x^2y''-(x^2+2x)y^2+(x+2)y=0, x > 0 if you know that y=x is a solution of...
Solve the DE: x^2y''-(x^2+2x)y^2+(x+2)y=0, x > 0 if you know that y=x is a solution of this equation.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT