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Quiz

MAT136H1 Quiz: MAT136H1 Differential Equations Review

4 Pages
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Department
Mathematics
Course Code
MAT136H1
Professor
Al- Faisal, Faisal

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Differential Equations Review
Question: True or False?
 is the most general solution to the differential equations

  
- False! We can get other solutions by changing the 6 in   to other numbers. It’s only
a solution, but not the most general solution to the differential equations.
Question: True or False?


    
   
  
 everywhere.


  
  
Square-rooting x could give both but    is not a function since it
won’t pass the vertical line test. However, it could give either or since
either one of them would be a function, but for this situation, it has to be in other
to satisfy the initial condition (pass through (0,3)).
Question: True or False?
Polynomials are never solutions to differential equations.

  
 
a polynomial.
Question: Suppose that    is a solution to the differential equation 
   is
increasing for all x, then the graph of is concave up for all .
  
  since  is increasing, so must be >0 too
Increasing here
graph of   general form not
taking into account initial conditions
true here
t
x

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Description
Differential Equations Review Question: True or False? = 6 4is the most general solution to the differential equations = 4. 4 - False! We can get other solutions by changing the 6 in =to other numbers. Its only a solution, but not the most general solution to the differential equations. Question: True or False? 1 If = and = 3 when t = 0,then is an increasing function of . when = 3, > 0,so the function increasing there, but you also want know if it s increasing everywhere. = 1 x Increasing here = 2 = + t true here 2 = + graph of =2 + general form not taking into account initial conditions Square-rooting x could give bot 2 + , but 2 + is not a function since it wont pass the vertical line test. However, it could gie ither 2 or 2 + since either one of them would be a function, but for this situation, it s to be 2 + in other to satisfy the initial condition (pass through (0,3)). Question: True or False? Polynomials are never solutions to differential equations. False! Example: with = + 1,the solution is 2 = + + ,which is a polynomial. 2 Question: Suppose that = () is a solution to the differential u= . If is increasing for all x, then the graph of is concave up for all . ( = > 0 > 0 since () is increasing, so must be >0 too
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