BT-202 (GS) – Mathematics-II
• Attempt any five questions.
• All questions carry equal marks.
a)Unit 1Solve x(dy/dx) + y = x³y⁶ using Bernoulli's
Solve x(dy/dx) + y = x³y⁶ using Bernoulli's
b)Unit 1Solve the differential equation (xeʸ+2y)(dy/dx) + y eʸ = 0 using Exact method
Solve the differential equation (xeʸ+2y)(dy/dx) + y eʸ = 0 using Exact method
a)Unit 1Solve (D²-6D+13)y = 8e³ˣ sin 2x
Solve (D²-6D+13)y = 8e³ˣ sin 2x
b)Unit 2Show that d/dx[xⁿ Jₙ(x)] = xⁿ Jₙ₋₁(x)
Show that d/dx[xⁿ Jₙ(x)] = xⁿ Jₙ₋₁(x)
Unit 2Solve (D²+1)y = x sin x using variation of parameters
Solve (D²+1)y = x sin x using variation of parameters
a)Unit 3Form the partial differential equation by eliminating the arbitrary functions from Z=(x+y)φ(x²-y²)
Form the partial differential equation by eliminating the arbitrary functions from Z=(x+y)φ(x²-y²)
b)Unit 3Solve (D²-DD'-6D'²)Z = xy
Solve (D²-DD'-6D'²)Z = xy
a)Unit 3Solve the partial differential equation yp - xp = z
Solve the partial differential equation yp - xp = z
b)Unit 4Show that u = e⁻ˣ(x sin y - y cos y) is Harmonic
Show that u = e⁻ˣ(x sin y - y cos y) is Harmonic
a)Unit 4Evaluate ∫(3x²+4xy+ix²)dz along y=x² from (0,0) to (1,1)
Evaluate ∫(3x²+4xy+ix²)dz along y=x² from (0,0) to (1,1)
b)Unit 4Find the Poles and Residues at each pole of f(z) = sin²z/(z-π/6)²
Find the Poles and Residues at each pole of f(z) = sin²z/(z-π/6)²
Unit 5Verify Green's theorem in the plane for ∮[(x²-xy³)dx+(y²-2xy)dy] where C is a square with vertices (0,0), (2,0), (2,2), (0,2)
Verify Green's theorem in the plane for ∮[(x²-xy³)dx+(y²-2xy)dy] where C is a square with vertices (0,0), (2,0), (2,2), (0,2)
a)Unit 5Find the directional derivative of f(x,y,z) = xy²+yz³ at point (2, -1, 1) in the direction of vector î+2ĵ+2k̂
Find the directional derivative of f(x,y,z) = xy²+yz³ at point (2, -1, 1) in the direction of vector î+2ĵ+2k̂
b)iUnit 4Write short note on: Cauchy's integral formula
Write short note on: Cauchy's integral formula
b)iiUnit 5Write short note on: Solenoidal and Irrotational
Write short note on: Solenoidal and Irrotational