Calculus Course/Differential Equations/2nd Order Differential Equations

2nd Order Differential EquationEdit

2nd Order Differential Equation is an equation that has the general form

 

Characteristic EquationEdit

2nd Order Differential Equations above can be rewritten as shown

 

Let

 

Then

 
 ) t
 
 
 

Case 1Edit

When

 

Then

 
 

Equation has one real roots

Case 2Edit

When

 

Then

 
 

Equation has two real roots

Case 3Edit

When

 

Then

 
 

Equation has two compex roots

Special CaseEdit

Case 1Edit

Differential Equation of the form

 
 

Roots of equation

 

Case 2Edit

Differential Equation of the form

 
 

Roots of equation

 

SummaryEdit

2nd Order Differential Equation

 

has roots depend on the value of  

  1.  
  2.  
  3.  

With