Unit – 4

Differential equations

Question and answer

Ans. Auxiliary equation are

2.

Ans. Its auxiliary equation is

Solution is

3.(

Ans. The auxiliary equation is

Hence the solution is

4. 

Ans. Given,

Auxiliary equation is

5.

Given,

For CF,

Auxiliary equation are

For PI

Ans. Auxiliary equation are

6.

Ans. AE=

Complete solution is

7.

Ans. The AE is

We know,

Complete solution is y= CF + PI

8. Solve in series the equation

Ans. 

Since x=0 is the ordinary point of the equation (1)

Then

Substituting in (1) we get

Equating to zero the coefficient of the various powers of x we obtain

Substituting these values in (2) we get

9.

Ans. We know

Differentiating with respect to z we get

Multiplying both sides by we get

Equating the coefficient of from both sides we get

10.

Ans. We know