Module 5

Ordinary Differential Equations of Higher Orders

Solve 

Sol:

Auxiliary equation

Solution is 

2.     Solve

Sol:

Auxiliary equation  

Complementary function

Complete Solution is

3.     Solve

Sol:

Auxiliary equation

C.F is

    []

   The Complete Solution is  

4.     Solve 

Solution:

The Auxiliary equation is

  The C.F is   y=

P.I

   The Complete Solution is 

5.     Solve

Sol:

The Auxiliary equation is   

  The C.F is

P.I

Now,  

   The Complete Solution is

6.     Solve 

Sol:

The auxiliary solution is

  The C.F is

Now,

  [Putting ]

Similarly, we find that

   The Complete Solution is

7.     Solve

Solution:

The auxiliary equation is  

The C.F is

Now, 

And 

   The Complete Solution

8.     Solve

Sol:

The auxiliary equation is  

The C.F is

Now, 

And 

   The Complete Solution

9.     Apply variation of parameter to solve   

 Sol:

Auxiliary equation is  

Solving quadratic equation 

C.F 

P.I 

 [Put  ]

Put

 The complete solution is

10. Solve

Sol:

The auxiliary equation is  

The C.F is

And,  

Now, 

And 

        And

    The Complete Solution is