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B192001 Pages: 3

solution.

OR
Solve the ordinary differential equation 2" - 397 — 49 + 69 = 0.
Solve the ordinary differential equation xy" + ‏اہر2‎ + xy = 0, given that
y= ಮ್ತು is a solution.

Module 11
By the method of variation of parameters, solve y” + 4y = tan2x.
Solve y" + 2y = x*e* ,
OR
Solve (x 3(2 — 4(x + 3)y' + ‏برع‎ = 3x.
Solve x*y" — 4xy' + 6y = ‏5ع‎
‎Module 111
Find the Fourier series of f defined by f(x} = x — x? in (- 1.1).
Expand f(x} = ‏ء‎ in the half range sine-series in 0 < x < छ.
OR

Obtain Fourier series for the function f(x} = [८०5४ |, -
Module 1V
Solver +5 2೭ = €>.

Find the general solution of {क — മുജ + y*(z —x)q = (x— y}z?.
OR
Solve (03 + D*D' — DD” — D'*)z = ‏کو‎ cos2y
Solve (D? + 3DD' + 2D")z = x?y?
Module V
A uniform elastic string of length 60 cm is subjected to-a constant tension of 2

Kg. If the ends are fixed, the initial displacement
u(x, 0) = 60x — ‏ع > 2,0ع‎ < 60 and the initial velocity is zero, find the

displacement function u(x,t}

OR

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