Lesson Summary
1.
We found general solutions of differential equations.
2.
We used initial conditions to find particular solutions of differential equations.
Multimedia Link
The following applet allows you to set the initial equation for
and then the slope field for that equation is displayed.
In magenta you'll see one possible solution for
. If you move the magenta point to the initial value, then you will see
the graph of the solution to the initial value problem. Follow the directions on the page with the applet to explore this
idea, and then try redoing the examples from this section on the applet.
Slope Fields Applet
.
Review Questions
In problems #1
–
3, solve the differential equation for
1.
2.
3.
In problems #4
–
7, solve the differential equation for
given the initial condition.
4.
and
.
5.
and
6.
and
7.
and
1
3
2
( )
3
f
8.Suppose the graph of f includes the point (-2, 4) and that the slope of the tangent line to f at x is -2x+4. Find f(5).

10
In problems #9
–
10, find the function
that satisfies the given conditions.
9.
with
and
10.
with
(4)
7
f
and
(4)
25
f
Review Answers
1.
2.
3.
4.
5.
6.
7.
8.
;
9.
10.

11
Initial Condition & Integration of Trig Functions Practice
1.Find the particular solution ( )yf xthat satisfies the differential equation and initial condition.
2.Find the equation of the function fwhose graph passes through the point.
'( )
6
10,
4,2
f
x
x
3.
Find the function
f
that satisfies the given conditions.
a.
"( )
2,
'(2)
5,
(2)
10
f
x
f
f
b.
2 3
"( )
,
'(8)
6,
(0)
0
f
x
x
f
f
4.
Integrate.
a.
(2sin
3cos )
x
x dx
b.
1
csc cot
t
t dt
c.
2
csc
cos
d
d.
2
sin
t
t dt
Answers:
x