Finding a particular solution of a differential equation

I already solved the homogeneous portion, and I need help solving the particular solution and of course combining the two to get the entire solution to the differential equation. Not too difficult - see attachment. Please use equation editor if possible. Thank you. --- Given that: dMS/dt = m(MN - MS) - pMS¬ ...continues

Solving a Particular solution to an Ordinary Differential equation

See attached problem. PLEASE NOTE!!! I have noted in the problem statement that I have solved the homogeneous portion of the differential equation, and I need assistance in solving for the particular solution and finally the whole solution. I have gotten 2 responses from other OTA's that are as follows: "The point is that y ...continues

Local/uniform Lipschitz constants

Determine if the following functions satisfy local or uniform Lipschitz condition. 1). te^y My work: I found d/dy (te^y) = te^y, and this is not bounded above for any value of y, so this made me conclude that it has locally Lipschitz condition since the Lipschitz constant here changes as the reagion changes? Am I right? ...continues

Initial value problem for systems of DE

Let Q(t) =< (less than or equal) C + integral from t_0 to t ( K(s) Q(s) ) ds, Where Q(t) is a nonegative function , C > 0 and K(s) >= 0. a).Show that: Q(t) =< Ce^( integral from t_0 to t ( K(s)ds) ), t >= t_0 b). What conclusion can be made if C = 0? ( Note that proof in a may fail is C = 0 ). I want a det ...continues

Systems of equations as transformations

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, given the "answer", show how to get there

(See attached file for full problem description and complete equations) --- dP/dt = m(ao¬¬¬)[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¬ "rai ...continues

Differential equations question

Please show all steps with some explanation. Thanks! Problem 2: 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 con ...continues

Differential Equations Test Review

I have completed problem 4 through b. Also, it can't be seen, but I have completed a on problem 7. I do need however help on the rest to prepare for my exam. For this to benefit me I will need the work and answers. (See attached file for full problem description)

Differential Equations Problems

(See attached file for full problem description) I have most of this completed, there is only a couple of spots where I need some help. 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, Thank you.

Use Maple to solve this exercise:

(See attached file for full problem description) --- 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. Co ...continues