Ordinary Diff Eq Exam Review Solutions 109

Ordinary Diff Eq Exam Review Solutions 109 - 1 Solutions...

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Unformatted text preview: 1 Solutions 111 13. . 14. . 15. 16. 17. A is true since satisfies the differential equation on each subinterval. B is true since the left and right limits agree at . C is not true since . 18. A is true since B is true since . satisfies the differential equation on each subinterval. . C is true since 19. A is true since B is false since since B is false. satisfies the differential equation on each subinterval. while . C is false 20. A is false since on the interval does not satisfy the differential equation . Since is false, B and C are necessarily false. 21. A is true since B is true since satisfies the differential equation on each subinterval. . C is false since while . D is false since C is false. 22. A is true since satisfies the differential equation on each subinterval. B is false since while . C and D are false since B is false. You cannot have a continuous derivative if the function is not continuous. 23. A is true since B is true since satisfies the differential equation on each subinterval. . C is true since . D is true since . 24. A is true since satisfies the differential equation on each subinterval. B is true since . C is true since . D is false since . 25. The general solution of on the interval is found by using the integrating factor . The general solution is and the initial condition gives , so that for . Continuity of at will then give , which will provide the initial condition for the next interval ...
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