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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST/SECOND SEMESTER B.TECH DEGREE
SPECIAL SUPPLEMENTARY EXAMINATION AUG/SEP 2016

MA-102 DIFFERENTIAL EQUATIONS

**Max Marks: 100 Duration: 3 hrs**

**PART A**

**Answer all questions Each carries 3 marks**

1.Find ordinary differential equation for the basis e^-x√2 , xe^-x√2

2.Reduce y"=y ' to 1^st order differential equation and solve.

3.Find the particular solution to (D^4—m^4)y=sin mx

4.Use variation of parameters to solve y"+y=secx

5.Find the Fourier coefficient "an" for the function f(x)=1+ lxl deﬁned in —3<x<3

6. Develop the Fourier Sine series of f(x)=x in 0<x<π

7. Obtain the partial differential equation by eliminating arbitrary function from x^2+y^2+z^2 =f(xy).

8. Solve y^2 zp + x^2 zq=xy^2

9.Solve ux+uy=0 using method of separation of variables

10.a ﬁnite string of length L is ﬁxed at both ends and IS released from rest with a displacement f (x). What are the initial and boundary conditions involved in this problem?

11. Write all the possible solutions of one—dimensional heat transfer equation

12. Find the steady state temperature distribution in a rod of length 30cm having the ends at 20° C and 80° C respectively.

**PART B**

**Answer one full question from each module**

**Module -1**

13. (a)Verify linear independence of e^-x cosx and e^-x sinx using Wronskian and hence solve the initial value problem y"+2y’+2y=0, y(0) = 0,y'(o)=15

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