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Ordinary Diff Eq Exam Review Solutions 12

# Ordinary Diff Eq Exam Review Solutions 12 - 14 1 Solutions...

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Unformatted text preview: 14 1 Solutions 17. There are two equilibrium solutions; ables and using partial fractions gives and simplifying gives and . Separating vari. Integrating which is equivalent to , a nonzero constant. Solving for gives . When we get the equilibrium solution . However, there is no which gives the other equilibrium solution . 18. There are no equilibrium solutions. Separating variables gives and integrating gives . Solving for gives , where . 19. Separating variables gives and integrating gives Thus , a real constant. 20. Separating variables gives . Simplifying gives . and integrating gives , a real constant. 21. In standard form we get from which we see that is an equilibrium solution. Separating variables and simplifying gives . Integrating and simplifying gives . 22. Separating variables gives a constant. and integrating gives , 23. The equilibrium solution is . Separating variables gives . Integrating and simplifying gives , real constant. 24. In standard form we get from which we see and are equilibrium solutions. The equilibrium solution satisﬁes the initial condition so is the required solution. 25. is the only equilibrium solution. The equilibrium solution satisﬁes the initial condition so is the required solution. 26. Rewriting we get from which we see that is an equilibrium solution. Separating variables gives and integrating gives , a constant. Solving for by taking the exponential of both sides gives , and allowing gives the equilibrium solution. The initial condition gives so . Thus . 27. In standard form we get ables and integrating gives so is a solution. Separating vari. Solving for gives ...
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