Solve the system y'=x x'=-x+ry-y^3 r is a real number. Solve for eigenvalues & stability of...

Solve the system

y'=x

x'=-x+ry-y^3

r is a real number. Solve for eigenvalues & stability of system. Show bifurcation value.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

x'=y-x+(x^3)/7 y' =-x Lyapunov function Ax^2+By^2 for A,B constant. Show stability & define circle for stability...

x'=y-x+(x^3)/7 y' =-x Lyapunov function Ax^2+By^2 for A,B constant. Show stability & define circle for stability area if attraction.

Formulate Newton’s method for the system x^3 = y y^3 = x Note that this system...

Formulate Newton’s method for the system x^3 = y y^3 = x Note that this system has three real roots (−1, −1), (0, 0) and (1, 1). By taking various initial points in the square −2 < x, y < 2, try to obtain the attraction regions of these three roots. P.S. An attraction region of a root is defined as the set of all initial points which will eventually converge to the root.

Find the eigenvalues and eigenfunctions of the Sturm-Liouville system y"+ lamda y = 0 o<x<1 y(0)...

Find the eigenvalues and eigenfunctions of the Sturm-Liouville system y"+ lamda y = 0 o<x<1 y(0) = 0 y'(1) = 0 (b) Show that the eigenfunctions Yn and Ym you obtained from the above are orthogonal if n not= m.

Solve the following system : z” + y ′ = cos x, y” − z =...

Solve the following system : z” + y ′ = cos x, y” − z = sin x, z(0) = −1, z′ (0) = −1, y(0) = 1, y′ (0) = 0.

Using matlab Find x and y that solve the following system: ln(x 2 + y) =...

Using matlab Find x and y that solve the following system: ln(x 2 + y) = 1 − y , xy = − √ x

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln...

Solve (1+e^x)dy/dx+(e^x)y=3x^2+1 Solve (x^3+y^3)dx+3xy^2 dy = 0 Solve (y-cos y)dx + (xsiny+x)dy = 0 Solve (1+ln x +y/x)dx = (1-lnx)dy Solve (y^2+yx)dx - x^2dy =0 Solve (x^2+2y^2)dx = xydy Solve Bernoulli's Equation x dy/dx + 2y = (x^4)(e^x)(y^2) Solve Bernoulli's Equation (1+x^2) dy/dx = 2xy +(e^x)(y^2) Solve IVP (3e^(x^2))dy + (xy^2)dx=0 ; y(1) = 2 Solve IVP dy/dx -2xy = e^(x^2) ; y(0)=0 Solve IVP (x^2+y^2)dx+(2xy)dy=0; y(1)=1 6. Mixture Problem Initially 40 lb of salt is dissolved in a large...

Solve the system by Laplace Transform: x'=x-2y y'=5x-y x(0)=-1, y(0)=2

Solve the system of equations: x+y^2=6y x-2y=-5

Solve for x,y,z if there if a solution to the given system of linear equations: x...

Solve for x,y,z if there if a solution to the given system of linear equations: x - 3y - 2z = -3 3x + 2y - z = 12 -x - y + 4z = 3

Consider the region R between the x-axis and the curve y = x^3 / 3 ,...

Consider the region R between the x-axis and the curve y = x^3 / 3 , between x = 0 and x = 1. (a) Calculate the surface area of the solid obtained by revolving R about the x-axis. (b) Write an integral for the the surface area of the solid obtained by revolving R about the y-axis

Subjects