5. Solve the initial value problem,
y" +y = 633 ,y(0) = 0, y’(0) =1
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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
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.
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
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
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.
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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
First-Order Linear DEs
The method for solving rst-order linear dierential equations gives the general solution
to the dierential equation. This means that every solution of the DE has the form of the
general solution! This also means that there are
3.3: Modeling with Systems of First-Order DEs
Sometimes we want our model to be a system of first-order DEs instead of a single DE.
Example 1: Radioactive Series. In the last class, we looked at modeling radioactive
decay of a substance. However,
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
Germantown Campus; Math Department
MATH 282: Differential Equations
Instructor: Kathryn Linehan
Office: Germantown campus, HT 221
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
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 Assignment 2
Instructions: Complete each problem using MATLAB to help you. You may need to do part of a problem
by hand and part using MATLAB. Any additional instructions for a problem will be listed below it.
Hand In: Unless otherwise spe