Normed Space, Compactness and Transformation

Let X be a normed space, I closed interval ( or half-open on the right) and a = inf I, b = sup I. Let h : I -> [0,infinity) be a continuous function such that integral ( from a to b ) h(t)dt < positive infinity where integral from a to b represents the improper integral when I is not closed. Let epsilon > 0 and ...continues

Solving an Ordinary Differential Equation

dP/dt = m(a0)[exp(-z1)t] - (z2/z1)P Solve this differential equation with a = ao at t=0 and a=a at t=t to show that: P = [mz1(a)] / [z2 - z12] + [mz1(ao) / (z12- z2)](a/ao)^(z2/z12) Where the last term in this equation is a/ao "raised to the power of" z2/z12 ---

Differential Equations : Uniqueness Theorem and Initial Conditions

Using uniqueness theorem, what can you conclude about the solution to the equation with the given inital conditions? dy/dt = f(y) y1(t) = 4 for all t is a solution y2(t) = 2 for all t is a solution y3(t) = 0 for all t is a solution inital condition y(0) = 1

Differential Equations : Fundamental Matrix, Eigenspaces, Eigenvectors, Homogeneous and Nonhomogeneous Equations and Characteristic Equations

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Systems of Differential Equations : Fundamental Matrix, Linearly Independent Solutions and Vectors,

Please see the attached file for the fully formatted problems. I need: (c) on #4 (c), (d) and check (b) on #6 (e) on #7 For this to help me with the test coming up I will need all work and answers,

Solving an IVP with Maple : Euler and Improved Euler Method

Use Maple to solve this exercise: Consider the following (IVP) logistic model p' = 10p(1-p) with p(0)=0.1 1. Solve this IVP and graph the solution over the interval [0, 10], Write down the Euler approximation, and Improved Euler approximation with step size h. 2. Compute and plot the first 100 points of the Euler method f ...continues

Differential equations...

Use the convolution integral method and hand calculation to come up with the exact formula for the solution of y'' [t] + 5y' [t] +6y[t]= 3.8E^(-t) with y [0]=2 y' [0]= -1

Inverse Laplace Transformation : g(t) = L^-1(G)(t) when G(s)=(1-e^-s)/(s+2)

Find the Laplace transform of g(t) = L^-1(G)(t) when G(s)=(1-e^-s)/(s+2) and create a piecewise definition of the solution.

Ordinary Diferential Equations and Initial-Value Problems : Method of Undetermined Coefficients, Variation of Parameters and General Solutions

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Differential Equation by Elimination : Eliminate the arbitrary constants from the equation: y = Ae^(2x) + Be^(-2x)

Eliminate the arbitrary constants from the equation: y = Ae^(2x) + Be^(-2x)