Consider the linear differential equation 
nxn
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there are so many methods to
solve that problem but suitable solution is that method.u can solve
by another method also .
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Consider the linear differential equation , with given matrix. Provide an example of for which the Lyapunov condition for the stability of the origin is satisfied and show the consequences on the O...
Consider a second-order linear homogeneous equation Suppose that are two solutions. Show that is also a...
Consider a second-order linear homogeneous equation
Suppose that
are two solutions. Show that
is also a solution to the equation (plug it in and use the fact
that
and
are solutions).
We were unable to transcribe this imageWe were unable to transcribe this imageZhg + th = Eh We were unable to transcribe this imageWe were unable to transcribe this image
Which of the following is the solution to the differential equation with the initial condition y(1)...
Which of the following is the solution to the differential
equation
with the initial condition y(1) = -1/2
A.
B.
C.
D.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Electrodynamics. Consider a linear medium where and are both zero in the region of interest. Show that the Maxwell...
Electrodynamics. Consider a linear medium where and are both zero in the region of interest. Show that the Maxwell's equations are invariant to the transformation where is a dimensionless constant and is a constant but arbitrary angle. In other words, if and are solutions of Maxwell's equations, show that and too. Consider the special case and thus show that, in this sense, the fields and can be interchanged. This property is often named the duality property of the electromagnetic field....
Consider the differential equation for , which models a population of fish with harvesting that...
Consider the differential equation for , which models a population of fish with harvesting that is governed by the logistic equation and a number of fish H caught and removed every unit of time (harvesting). Here the parameters r, K, and H are all positive. a) Assume that . Draw the phase plane. b) Assume that . What happens to the population of fish as t increases? Can I have a step-by-step walkthrough on how to solve these two. I...
Provide the process for obtaining the solutions of the first equation, which is the equation of step response, and the...
Provide
the process for obtaining the solutions of the first equation,
which is the equation of step response, and the solutions for the
cases of ζ > 1, ζ =1, and ζ <1.
de, (t)2 d'e,(t) We were unable to transcribe this imagedt C dt R C 2 0 and θ are given by the following eq 2 0
de, (t)2 d'e,(t)
dt C dt
R C 2
0 and θ are given by the following eq 2 0
8.2.6 Given that Pn(x) = x and Q0(x) = 12ln(1+x1-x) are solutions of Legendre’s differential equation (Table 7.1) co...
8.2.6
Given that Pn(x) = x and
Q0(x) =
12ln(1+x1-x)
are solutions of Legendre’s differential equation (Table 7.1)
corresponding to different eigenvalues.
(a) Evaluate their orthogonality integral
-11x2ln(1+x1-x)dx .
(b) Explain why these two functions are not orthogonal, that is,
why the proof of orthogonality does not apply.
It's in Mathematical Methods for Physicists 7e, Arfken ch8.2
Hermition operator
Please help.
Please explain as much as possible and solve it step by
step.
Thank you so much.
Given that 8.2.6...
Linear statistical models For ridge regression, we choose parameter estimators b which minimise where is a constant penalty parameter. Show that these estimators are given by 7n i=1 We were unable...
Linear statistical models For ridge regression, we choose parameter estimators b which minimise where is a constant penalty parameter. Show that these estimators are given by 7n i=1 We were unable to transcribe this imageWe were unable to transcribe this image 7n i=1
We were unable to transcribe this imageThe graph of the function f(r) is (1 point) (the horizontal axis is x.) Given the differential equation z'(t) = f(z(t)). List the constant (or equilibrium)...
We were unable to transcribe this imageThe graph of the function f(r) is (1 point) (the horizontal axis is x.) Given the differential equation z'(t) = f(z(t)). List the constant (or equilibrium) solutions to this differential equation in increasing order and indicate whether or not these equations are stable, semi-stable, or unstable
The graph of the function f(r) is (1 point) (the horizontal axis is x.) Given the differential equation z'(t) = f(z(t)). List the constant (or equilibrium) solutions to...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt ...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a f...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
Consider a second-order linear homogeneous equation
Suppose that
are two solutions. Show that
is also a solution to the equation (plug it in and use the fact
that
and
are solutions).
We were unable to transcribe this imageWe were unable to transcribe this imageZhg + th = Eh We were unable to transcribe this imageWe were unable to transcribe this image
Which of the following is the solution to the differential
equation
with the initial condition y(1) = -1/2
A.
B.
C.
D.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Provide
the process for obtaining the solutions of the first equation,
which is the equation of step response, and the solutions for the
cases of ζ > 1, ζ =1, and ζ <1.
de, (t)2 d'e,(t) We were unable to transcribe this imagedt C dt R C 2 0 and θ are given by the following eq 2 0
de, (t)2 d'e,(t)
dt C dt
R C 2
0 and θ are given by the following eq 2 0
8.2.6
Given that Pn(x) = x and
Q0(x) =
12ln(1+x1-x)
are solutions of Legendre’s differential equation (Table 7.1)
corresponding to different eigenvalues.
(a) Evaluate their orthogonality integral
-11x2ln(1+x1-x)dx .
(b) Explain why these two functions are not orthogonal, that is,
why the proof of orthogonality does not apply.
It's in Mathematical Methods for Physicists 7e, Arfken ch8.2
Hermition operator
Please help.
Please explain as much as possible and solve it step by
step.
Thank you so much.
Given that 8.2.6...
We were unable to transcribe this imageThe graph of the function f(r) is (1 point) (the horizontal axis is x.) Given the differential equation z'(t) = f(z(t)). List the constant (or equilibrium) solutions to this differential equation in increasing order and indicate whether or not these equations are stable, semi-stable, or unstable
The graph of the function f(r) is (1 point) (the horizontal axis is x.) Given the differential equation z'(t) = f(z(t)). List the constant (or equilibrium) solutions to...
Problem 5. Consider the following second order linear differential equation f"(t)-f'(t) +f(t) kt which models a forced oscillation in a damping material. For example, imagine moving your hand back and forth underwater. Write this equation as a set of coupled first order equations by doing the following: ·Define a new function g = f'(t). This gives you one of the two coupled equations. . Use the given ODE, g, and its derivatives to write the second first order equation. Both...
Discretization, ODE solving, condition number. Consider the differential equation 5y"(x) - 2y'(x) +10y(x)0 on the interval x E [0,10] with boundary conditions y(0)2 and y (10) 3 we set up a finite difference scheme as follows. Divide [0,10] into N-10 sub-intervals, i.e. {xo, X1, [0,1,. 10. Denote xi Xo + ih (here, h- 1) and yi E y(x). Approximate the derivatives as follows X10- 2h we have the following equations representing the ODE at each point Xi ,i = 1,...
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