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A2801 5

Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER B.TECH DEGREE EXAMINATION, APRIL 2018

Course Code: MA102
Course Name: DIFFERENTIAL EQUATIONS

PART A

Answer all questions, each carries 3 marks.
Solve the initial value problem xy’ = y - 1,y(0) = 1
Solve the following differential equation by reducing it to first order xy" = 29.
Find the particular integral of (D? + 3D + 2)y 3.
Find the particular integral of y" + y = sinx.
Obtain the Fourier series expansion for the function f(x) = x inthe range = -7 <
೫ < 7.
Find the Fourier sine series of the function f(x) = mx - x? in the interval (0, 7)
Form a partial differential equation by eliminating the arbitrary function in xyz =
O(x+y+z)
Solve 7 + $ - 2६ ௪512,
Solve one dimensional wave equation णि k < 0.
Solve x 2 = —u = 0, ५८८, 0) = 66735 using method of separation of variables.

Find the steady state temperature distribution in a rod of length 30cm if the ends are
kept at 20°C and 80°C.
Write down the possible solutions of one dimensional heat equation.
PART B
Answer six questions, one full question from each module.
Module I

3 1
Verify that the given functions x2, x are linearly independent and form a basis of
solution space of given 001 4529" - 3y = 0.

Solve the boundary value problem:
y"—10y'+25y=0, yO)=1, ೫(1) = 0.
OR
Find the general solution of ‏"برج + “تبر‎ + y = 0.
Find a fundamental set of solutions of 2t?y" + 3ty’ — y = 0,t ಆ 0. Given that
y(t) = ತ is a solution.
Module 11
Find the particular integral of + 34 + 2y = 400522.
Solve ey நரம +9y = ಕ using method of variation of parameters.
dx? dx x

OR
Solve ८29 — xy’ — 3y = x? Inx
Solve ^“ -- 2)“ + 5y” — ‏ابرق‎ + 4y = e*.

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Duration: 3 Hours

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