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¬
MN¬ (0) = MS (0) = 0
And using:
M¬N + MS = [Po/(r + p)](ert - e-pt)
Show that

MS(t) =

BY SOLVING THE DIFFERENTIAL EQUATION FOR dM¬s¬/dt with a homogeneous and particular solution.

Using the MN + MS equation to solve for MN¬ in terms of MS gives the differential equation to be solved as:

I have already solved the homogeneous solution to this differential equation to get that :

MS = C1e-(2m+p)t where C1 is the constant of integration.

What I need is the particular solution, and the hint I received in class was to start by assuming that MS = C2ert + C4e-pt

And of course the solution will be the addition of the homogeneous and particular solutions, using the boundary conditions given above that MS¬(0)=MN(0) = 0
---

(See attached file for full problem description and equations)

... Dear student, please refer to the attachment for the solutions. Problem: Find the solution of the differential equation dy/dx=x^3 -x with the initial condition ...

... Question 14: (1 points) Find the solution of the following differential equation... equation we solved in question 2, for which we found the explicit solution. ...

...Finding PS.(Particular solution). ...Find a and b: ... I have found general solutions and particular solutions to non homogeneous second order and higher order ...

... c) Find the solution y=f(x) to the given differential... now the solution is y=f(x)=1/(x^2-1/2). Differential Equations, Tangents and Solutions are investigated. ...

... 4. Find a second order ODE whose solution is a ... Fourier series, Fourier Transform and Partial differential equation 5. Write the Fourier series for ()cosftt ...

... Begin by finding expressions for y′ and y ... the same as the homogeneous solutions found in part a ... Using the Method of Undetermined coefficients find a particular ...

... a number for x in both your solution and the given ... In this example you will find a simple ordinary ... The dx and dy found in the equation denote the ...

... 2-4w^2)] / 2 Values of n and w can be found from the ... n^2- 1)] = - wn +/- iw*sqrt (1 - n^2)] Solution is: x ... m and dx/dt = 0. Using this info, one can find A and B ...

... y (10) = 75.9 sec An alternative method for finding the time ... then in order to find the solution in the ... Finally to find unknown constant B we can substitute for ...

Finding The Solution For Differential Equations. Find the general solution of the differential equation: y'' + y ... Now u1 and u2 can be found by using previous ...