a)Unit 1Solve (1+y²)dx = (tan⁻¹y - x)dy using Leibnitz linear method
a)Unit 1
Solve (1+y²)dx = (tan⁻¹y - x)dy using Leibnitz linear method
b)Unit 1Solve (eʸ+1)cos x dx + eʸ sin x dy = 0
b)Unit 1
Solve (eʸ+1)cos x dx + eʸ sin x dy = 0
Previous Year Question Paper
BT-202 (GS) – Mathematics-II
December 2023•COMMON•SEMESTER-2
December 2023
Max Marks: 70
Duration: 3 Hours
Instructions:
• Attempt any five questions.
• All questions carry equal marks.
a)Unit 1Solve (D² - 4D + 3)y = cos 2x
a)Unit 1
Solve (D² - 4D + 3)y = cos 2x
b)Unit 2Show that J₁/₂(x) = √(2/πx) sin x
b)Unit 2
Show that J₁/₂(x) = √(2/πx) sin x
Unit 2Solve (D²+9)y = tan 3x by using method of variation of parameters
Unit 2
Solve (D²+9)y = tan 3x by using method of variation of parameters
a)Unit 3Solve the partial differential equation (x-y)p + (x+y)q = 2xz
a)Unit 3
Solve the partial differential equation (x-y)p + (x+y)q = 2xz
b)Unit 3Solve (p²+q²)y = qz by using Charpit's method
b)Unit 3
Solve (p²+q²)y = qz by using Charpit's method
a)Unit 3Solve (D²+4DD'-5D'²)Z = sin(2x+3y)
a)Unit 3
Solve (D²+4DD'-5D'²)Z = sin(2x+3y)
b)Unit 4Determine p so that f(z) = ½ log(x²+y²) + i tan⁻¹(px/y) is analytic function
b)Unit 4
Determine p so that f(z) = ½ log(x²+y²) + i tan⁻¹(px/y) is analytic function
a)Unit 4Show that u(x,y) = eˣ cos y is Harmonic. Determine its Harmonic conjugate
a)Unit 4
Show that u(x,y) = eˣ cos y is Harmonic. Determine its Harmonic conjugate
b)Unit 4Find the residue of Zeᶻ/(Z-1)³ at its pole
b)Unit 4
Find the residue of Zeᶻ/(Z-1)³ at its pole
Unit 5Verify Gauss divergence theorem for F = x³î + y³ĵ + z³k̂ taken over the cube bounded by x=0, x=a, y=0, y=a, z=0, z=a
Unit 5
Verify Gauss divergence theorem for F = x³î + y³ĵ + z³k̂ taken over the cube bounded by x=0, x=a, y=0, y=a, z=0, z=a
a)Unit 5Prove that curl(rⁿ r) = 0
a)Unit 5
Prove that curl(rⁿ r) = 0
b)iUnit 4Write short note on: Cauchy Riemann equations
b)iUnit 4
Write short note on: Cauchy Riemann equations
b)iiUnit 5Write short note on: Stokes theorem
b)iiUnit 5
Write short note on: Stokes theorem