Ordinary differential equations

Ordinary differential equations. Meet again with  4learnmath blog about  the material elementary school mathematics, high school math materials, , and  college mathematics. In this post, 4learnmath will share about questions ordinary differential equations. the following is the questions.

2.   Show that y = sin x - cos x is a solutions Initial value problem :
      y'+y =0, y(0)=-1 and y'(0)=1

3.   Specify the differential equations wich can be formed form the equations :

4.  Be given initial value problem :

      Wheter the initial value problem to have single solutions? explain.

5.  Complete the following differential equations :

 

 

6. Complete the following initial problem :

   

 

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Sorted nature of the real number

Sorted nature of the real number is the title of this post. Meet again with  4learnmath blog about  the material elementary school mathematics, high school math materials, , and  college mathematics.

Sorted nature of the real number
a linear sequence of real number system through the creation of a collection compiled in R, called the assemblage positive real number.
Definition.
a nonempty subset P of R called positive real number :
1. for each a,b  element P apply a+b element P
2. for each a,b  element P apply a.b element P
3. for each a element R,  exactly one statement met a element P or -a element P or a= O.
    (trichotomy)
furthermore if a element P said a positive number and writed a>0. If a element P Union {0} said  a non negative number and writed a>= 0. If -a element P said a negative number and writed a<0 , if -a element p union {0} said a non negative number and writed a<= 0.

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