• Attempt any five questions.
• All questions carry equal marks.
Solve cos x (dy/dx) = y(sin x - y) using Bernoulli's
Solve the Linear differential equation sin 2x (dy/dx) - y = tan x
Solve (r + sinθ - cosθ)dr + r(sinθ + cosθ)dθ = 0
Solve the differential equation (D³ - 7D² + 14D - 8)y = eˣ cos 2x
Solve (D² + 4)y = tan 2x by using method of variation of parameters
Show that r/r³ is solenoidal
Show that vector (x²-yz)î + (y²-zx)ĵ + (z²-xy)k̂ is irrotational. Find its scalar potential
Verify Green's theorem for ∮[(3x²-8y²)dx + (4y-6xy)dy] where C is region bounded by x=0, y=0 and x+y=1
Show that f(Z) = Z\bar{Z} is differentiable but not analytic at origin
Show that u(x,y) = e⁻²ˣ sin 2y is harmonic and determine its Harmonic conjugate
By Residue theorem, Evaluate ∮ tan z/(z²-1) dz, where C:|Z|=2
Using Cauchy integral theorem, evaluate ∮ e²ᶻ/[(z-1)²(z-3)] dz, where C is circle |Z|=2
Solve x²p² + y²q² = z²
Solve (D² - 4DD' + 4D'²)Z = cos(x-2y)
