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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).
Use D-operators to find a particular solution to the differential equation: y^n + y' - 2y= e^-2x
Find the transient and steady-state currents in the RLC circuit with L= 5 henrys, R= 10 ohms, C=0.1 farad and E=25sint t volts.
The heat transfer problems dealing with the radiation phenomena face nonlinear boundary conditions. Use the SHOOTING method to solve the governing equation.
Use the Laplace properties and the s-shifting theorem to solve the differential equation yn-4y'+8y=2e-2t
Based on results of model I was to consider three scenarios. First, triple Education expenditure. Second, double PC's. Third, double Phones.
I know that a standardized regression coefficient is able to provide us with a ranking of the relative importance of each independent variable in a regression .
The slop of the regression line indicates that for every penny increase in price, she reduces her sales by about 0.26kg a day.
X is the time since a pebble was dropped down a well, and y is the distance it has fallen.
Demonstrate using regression functions by explaining what a regression function is.
In California in 1990 the population was 29, 839, 250. what is the prediction of california's population in the long-run?
What will be the estimated sales if there are 7 showings in a week? And for 20 showings?