#4
#3
1
#9
#11
7
Group #2
p#
Gr
ou
p#
u
Gr o
MAT 146
#6
#10
Monday, Oct 24, 2016
#5
#12
Seating by Group
Gr
ou
p
#8
Monday, Oct 24, 2016
MAT 146
Example 1
Generate a numerical approximation
for a solution to the differential
equation y¢ = 2x - y at x = 5/4. Use Euler’s
Method, with step size ¼ and initial
condition that (0,0) satisfies y.
Monday, Oct 24, 2016
MAT 146
Monday, Oct 24, 2016
MAT 146
Use Euler’s Method to approximate the
value of y(4/10) for the differential
equation y! = 2xy , with initial condition
y(0) = 1 and step size ∆x = 1/10 units.
Create a table to organize your
calculations. Use your results to plot
tangent-line segments that create a
graphical approximation to the
differential equation.
Monday, Oct 24, 2016
MAT 146
Monday, Oct 24, 2016
MAT 146
Monday, Oct 24, 2016
MAT 146
Use Euler’s Method to approximate the
value of y(1.4) for the differential
equation y! = x ² xy , with initial condition
y(1) = 0 and step size 0.1 units. Create
a table to organize your calculations.
Monday, Oct 24, 2016
MAT 146
Monday, Oct 24, 2016
MAT 146
Solve for y: y’ = −y2
Suppose we also know that (0,1) satisfies the
solution function.
Monday, Oct 24, 2016
MAT 146
We can determine analytical solutions to
differential equations of certain types.
We can use separation of variables when a
differential equation is of the form
dy
y¢ =
= g(x)× f (y).
dx
Monday, Oct 24, 2016
MAT 146
Solve for y: y’ = 3xy
Monday, Oct 24, 2016
MAT 146
Solve for z:
Monday, Oct 24, 2016
dz/ +
dx
MAT 146
x+z
5e
=0
Solve for P using separation
of variables, knowing (1,2)
satisfies your solution:
dP/
Monday, Oct 24, 2016
1/2
=
(2Pt)
dt
MAT 146
Use separation of variables to solve the
dy
3x 2
differential equation dx = y + cos ( 2y) .
Monday, Oct 24, 2016
MAT 146