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Total No. of Questions : 5
Total No. of Printed Pages : 3
EY-308
B.Tech. IIIrd Semester (New Scheme) Inform. Tech.
Examination, 2023-24
Mathematics - II
Paper - IT-301
Time : 3 Hours
[Maximum Marks : 60
Note :- Attempt any two parts from each questions. All questions carry equal marks.
1.
(a)
Solve Sec x dy/dx = y + sin x
(b)
Solve: d3y/dx3 + d2y/dx2 - dy/dx - y = cos 2x
2.
(a)
Solve: x d2y/dx2 + 5x dy/dx + 4y = x log x
(b)
Solve by the method of variation of parameter's (D2 + 1)y = x; D = d/dx
(c)
Solve: d2y/dx2 - 2 tan x dy/dx + 5y = ex sec x
(d)
Solve: d2y/dx2 - cot x dy/dx - (1 - cot x)y = ex sin x
3.
(a)
Solve using Lagrange's method xzp + yzq = xy
(b)
Solve by charpit's method Px + qy = pq
(c)
Solve (D2 - 2DD' + D'2)z = 12xy
where D = â/âx, D' = â/ây
where D = â/âx, D' = â/ây
4.
(a)
Prove that the function f(z) = z2 is analytic function.
(b)
Integrate z2 along the straight line OA and also the path OBA consisting of two straight line segments OB and BA where O is the origin, B is the point z = 3 and A the point z = 3 + i.
(c)
Write the following (without proof)
- Cauchy - Riemann equations.
- Cauchy - Goursat theorem
- Cauchy - Integral formula
5.
(a)
Show that the vector F is irrotational if F = (sin y + z)i + (x cos y - z)j + (x - y)k
(b)
Prove that div grad rm = â2 rm = m(m+1)r(m-2)
(c)
Evaluate âĢâĢS (yzi + zxj + xyk)ds where S is the surface of the sphere x2 + y2 + z2 = 1 in the first octant.