advertisement

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