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Find the inverse Laplace transform of each of the following functions: (a) F(s) = s3/s4 + 4a4
For n > 0; find the solution to the boundary value problem -?u=(n/p)e-n(x2+y2),x2+y2<1,u(x,y)=0,x2+y2=1.
Find a partial differential equation whose characteristic curves are the lines x-y=a, x+2y=b where a,b are arbitrary real constants
Suppose the boundary conditions are that u(x,y) vanishes on the lines x=0 ,x=3, y=0, and y=2. Derive the corresponding boundary conditions for f and g.
Find solutions to the given Cauchy- Euler equation-xy'+ y =0 (b) x2y'' + xy'+y =0 ; y(1) =1, y'(1) =0
Let h=.1 use euler & improved to approximate to get "Phee" of .1, phee of.2, and phee of .3
Suppose that a rabbit is initially at point (0,100) and a fox is at (0,0). Suppose that the rabbit runs to the right at speed Vr = 5 ft/sec and the fox.
The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second.
The intake rate I1 of lead into the blood from the GI tract and the lungs is a constant or a piecewise continuous function of time.
Show that for any integer n=1, Xn(x) = e-x sin nx is an eigenfunction of the Sturm-Liouville problem for X and determine the corresponding eigenvalue.
Determine if the following system has nay non-constant solutions that are bounded, i.e. do not run off to infinity in magnitude x' = x(y - 1)
Let x: [0, infinity) -> R and y: [0, infinity) -> R be solutions to the system of differential equations: x' = - x y' = - sin y
Find the steady-state solution for the differential equation (dI/dt)+12I= 65cos(5t-30°)+ 45sin(9t +30°).
Use Laplace Transforms to solve the following Differential Equation. y?-8y'+20y=tet ,y (0) = 0 , y ‘(0) = 0
Make the substitution t = ln(x) and write the ODE with independent variable t.
I need them linearized so that I can use Gauss-Seidel iteration in Matlab to create the butterfly effect.
If the new width is s - 6 centimeters, then what are the new length and height?
What is the velocity and distance at the end of one minute?
As a system of 1st order ODEs and verify that there exists a global solution by invoking the global existence and uniqueness Theorem.
Solve the linear equation (?-A)u=0 to get the eigenvector(s) u= [u1,u2]2
Two tanks A and B, each of volume V, are filled with water at time t = 0. For t > 0, volume v of solution containing mass m of solute flows into tank A .
Determine the power series expansion of the solution u = [summation] b(k) x^k of u' = u^3 , u(0) = 1 and show that a(k) >= b(k).
Find a Lipschitz constant, K, for the function f(u, t) = u3 + tu2 which shows that f is Lipschitz in u on the set 0 = u = 2, 0 = t = 1.
Comparison of methods at different time steps (weaknesses and strengths of both methods)
Use a fourth-order Runge-Kutta (RK4) method with h = 1 to approximate the velocity v (5).