The dependence of the velocity v of a particle upon time t obeys the differential equation:
dv/dt = -av^2 - bv
where a>0, b>0 are constants. The initial condition is v(0) = V0 where V0 is the velocity at time t=0.
a. What is the order of this equation? Is it linear or non-linear?
b. Find the general solution of the equation in the case where a=0, b=/=0 and use this to find a solution satisfying the initial condition
c. Find the general solution of the equation in the case where b=0, a=/=0 and use this to find a solution satisfying the initial condition.
d. Write 1/(av^2 + bv) = A/v + B/(av+b) and determine the coefficients A and B.
e. Hence or otherwise find a general solution to the equation for v. Show that your solution leads to the following equation for v(t) which satisfies the stated initial condition:
(aV0 + b)/V0 exp (bt) = (av(t) + b)/ v(t)
f. Rearrange this expression to find an expression for v(t).

Hello and thank you for posting your question to Brainmass.
The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

Feedback is always appreciated.

The order of the equation is determined by the highest order of the derivative.
In this case the highest order of the derivative is 1, therefore this is a first order equation.
Let be a solution of the equation
The equation is linear if is a solution as well, where is an arbitrary constant.
The equation is:
(1.1)
When we plug (1.1) into (1.2) we get:

(1.2)
Obviously, ...

Solution Summary

The solution shows in detail how to separate the non-linear equation and use partial fraction method to integrate it.

For each of the following ordinairy differentialequations, indicate its order, whether it is linear or nonlinear, and whether it is autonomous or non-autonomous.
a) df/dx +f^2=0
(See attachment for all questions)

Use D-operators to find a particular solution to the differentialequation:
y^n + y' - 2y= e^-2x
Hence write its general solution. Find the solution that satisfies the initial conditions:
y(0) = 1/3, y'(0) = -1/3

Find the general solution of the second orderdifferentialequation y'' - y' - 6y = e^-3x
This one is quite long winded, and I am pretty sure that I am getting yh right but can't seem to get close to yp. I think this is a D.R.A.E?

Linear Partial DifferentialEquation (II)
Non- Homogeneous Linear Partial DifferentialEquation with Constant Coefficients
Problem: Find the solution of the equation (D2 - D'2 + D -

Hi there, I have a question regarding ODE which can be located here http://nullspace8.blogspot.com/2011/10/e2.html. can someone please take a look? Full working step by step solution in pdf or word please. If you think the bid is insufficient and you can do it, please respond with a counter bid. Thank you.

I have this differentialequation.
y' = x^2*cos^2(y).
I don't know if it's a separable differentialequation or a firstorderdifferentialequation. Please show me the steps in how to solve it.
Thank you.

Hi,
Please help working on
section 1.1 problems 2,4,8,14,16
section 1.2 problems 6,10,20,24,27
thank you
See attached
Classify each as an ordinary differentialequation (ODE) or a partial differentialequation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ODE, ind

Please find the general solution of the nonhomogenous second order linear differentialequation below by following these steps:
1. Find the general solution y= C1y1 + C2y2 of the associated homogenous equation (complementary solution)
2. Find a single solution of yp of above.(particular solution).
3. Express the general so

Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A are used. It is observed that 10 grams of C are formed