Total points: 65 1. Explain what is meant by the phrase "first-order differential equation." 2....

Question

Total points: 65 1. Explain what is meant by the phrase "first-order differential equation." 2. Determine whether each of the functions below is a solution of the differential equation ys-t-y=0? (4 points' y=c,e' +c2ert b. y=c,sint +c2cost

005_f7qhajo-srrzidqx.docx

Robert · Accepted Answer

Sol: 
 First – order differential equation or an ordinary differential equation is an equation containing 
a function of one independent variable and its derivatives.
Sol:
(    )    
the characteristic equation is       , whose roots are     . 
Hence the general solution of the given equation is
Sol: 
a. Integrating factor =  (∫  )     
Multiplying it on both sides, we get, 
         
  
    
 
 (   )
  

    
 
Integrating on both sides, we get, 
     ∫
  
    
   
             (    )    
   
  (    )
  
   
Given  ( )      
  ( )
  
  (    )
  
         
b.
Integrating on both sides, we get, 
        ∫      
   
 
   
Given  ( )     
         
 
 
( )
         
   
 

Sol: 
 ( )  
  
√    
 
Consider the function,

Total points: 65 1. Explain what is meant by the phrase "first-order differential equation." 2. Determine whether each of the functions below is a solution of the differential equation ys-t-y=0? (4...

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