2. Consider the population model
95:0.15(1——P— 5—1 P
dt 250 75
Where P(t)is the population at time t
a) For whatvalues of P is the population in equilibrium?
b) For what values of P is the population increasing?
c) For what values of P is the population d
You must show all work in order to receive full credit. Follow the instructions posted on the
quiz module page on the course Blackboard site.
1. State the order of the following DE. Also determine if the DE is linear or nonlinear.
1. For the system a: = B 31] ,YY(t)= [:8]
3) Compute the eigenvalues of [I _1
'b) For each eigenvalue, compute an associated eigenvector.
c) For each eigenvalue, specify the equation of the corresponding
straight line solution
d) Write the general sol
Matlab Project #2
Name: Faisa Mohamed
Draw a direction field for the system
First use dsolve to plug in dx and dy
Second I used meshgrid and write in the x-axis, y-axis and space between the straight lines
Third I made U=dx and V
MA 282-Assignment #1: First Order Differential Equations -Part-1
The standard form for a first-order differential equation is
= (, ) . A solution to this
equation is a differentiable function ()of the independent variable that satisfies
() = (, ().
MA 282-Assignment #3: Numerical Solutions-the MATLAB Command ode45
So far we have been using examples where the command dsolve was capable of producing
explicit solutions of the differential equations.
Now consider the IVP: = 2 0.2 sin() , (0) = 2.
HA (ms: SINGH *
1. An object is taken out of the oven that is set at a .
temperature of 370°F and taken to a room that is at a
temperature70°F. After 5 minutes, the temperature of
the object i525O°F.
a) Use the Newton’s law of cooling to wri
a) Find a formula for the solution of the differential
dt (y+2)2 , y(0)=l
b) State the domain of the definition of the solution.
fun) Ayﬁt W6“; K7
Cy +1)3 1 t +4
/ ﬁlo) 711
J 3 . C
2‘: C C C}
~\> (Vi 1J‘J ~ tfq
3. For a certain logistic growth model, the growth rate
parameter is k = 0.35 and the carrying capacity N = 2700.
If 150 units of this population is harvested each year and
the initial value of the population is 2100 Le. P(0)=2100,
Use a qualitative a
6 . Consider the differential ed‘UatiOn g;— 5y? — 2Y —‘8' :1, VI
a) Sketch the phase lines. Identify the equilibrium points
as source, sink or nodes .
b) Using only one set of axes, sketch graphs of the .
solutions that cOrrespond to the initial condition
MA 282-Assignment #2: First Order Differential Equations -Part-2
1. Understanding the quiver command
The quiver command allows us to draw vectors in the plane 2 :
For instance, if we wish to draw the two vectors a = < 2,3 > and = <
5. Solve the initial value problem,
y" +y = 633 ,y(0) = 0, y’(0) =1
\— [ft/91(5) I ‘Cmcix
L [€371 WU}; » L @415 may :0
L Dux S\ s Cngjasj) Ma) y La)
LxC/HDy-Séﬂvjﬁs LEW/29%] /[,0]: O
M) a Hwy
L,L,'/)Crc¢)5+“§"CL,¢L/o< 5) [IQ
CQH) (Liv , L'eﬂ‘i “
MATLAB Tutorial: Part 2
Finding Roots of Equations
MATLAB can find roots of equations!
One way to find roots is to use the solve( ) command.
In these examples we find the roots
of f(x) = x2 2x 3, g(x) = 2x3 2x2,
and h(x) = x3+ 1.
If a zero has mult
MATLAB Tutorial: Part 1
This is what the MATLAB environment looks like.
We can type commands at the command prompt.
We can use MATLAB like a calculator!
Just type in expressions at the comman
Germantown Campus; Math Department
MATH 282: Differential Equations
Instructor: Kathryn Linehan
Office: Germantown campus, HT 221
5. The following MATLAB code performs Eulers method for an IVP.
Note: MATLAB starts indexing with 1 and not 0! When we do Eulers method by hand, we call
our initial values and . MATLAB calls its initial values and . So, for example, if by hand