Math 308
Due: Feb 3rd
Spring 2016
Find the general solution of the ODE:
1. (x2 − 9) dy + xy dx = 0
2. x dy + (y − y 2 ) dx = 0
3. cos3 x y 0 − 3 sin x cos2 x y = 1
4 cos2 x sin x y 0 + cos3 x y = 1
5. y 0 + 2x y = arctan x
6. y 0 =
y − xy
x
7. y 0 =
y2
Hint using that
ex + e−x
8. y 0 =
x2 − y 2
2xy
1
ex +e−x
=
ex
e2x +1
may help
9. (x2 − 1) y 0 + 2x y = (2x + 1)2
10. y 0 =
1
Hint let u = y − x then solve the corresponding ODE for u
y−x
11. y 0 =
2y
5y − 2x
1
Math 308
12. y 0 =
Due: Feb 3rd
Spring 2016
xy 2 − cos x sin x
y(1 − x2 )
Provide a solution for the following (show all work)
13. Show that any separable equation is also an exact equation.
14. The CSI Problem: Consider Newton’s law of cooling
dy
= k(y − T )
dt
Where k is a constant and T is the surrounding temperature. A victim’s body is
found dead in a hotel room that is keep at 72o . The body temperature is 96.5o when
the CSI enters the crime scene. The CSI collects evidence for an hour then checks
the body temperature to now be 95.8o . Given this information determine how long
ago did the victim died.
2