BT-202 (GS) – Mathematics-II

Solve (e^x+1)cos x dx + e^x sin x dy = 0

Solve (D²-5D+6)y = 4e^x+5

Solve x²(d²y/dx²) + 5x(dy/dx) + 4y = x log x

Solve in series Legendre's differential equation (1-x²)(d²y/dx²) - 2x(dy/dx) + 2y = 0

Solve (D²+a²)y = tan ax by using method of variation of parameters

Eliminate the arbitrary function f from the relation z = y² + 2f(1/x + log y)

Solve the partial differential equation ∂²z/∂x² - ∂²z/∂y² = x²y

Solve (y+z)p + (x+z)q = x+y

Find all values of K such that f(z) = e^x(cos ky + i sin ky) is analytic

Evaluate ∫(3x²+4xy+ix²)dz along y=x² from (0,0) to (1,1)

If f(z) = 1/((z-1)(z-2)²) find residue of all poles

If r is the position vector of any point in space, prove that r^n r is irrotational

Find the workdone by force F = zî + xĵ + yk̂ when it moves a particle along the arc of curve r = cos t î + sin t ĵ - t k̂ from t=0 to t=2π

Verify Stokes theorem for F = (x²-y²)î + 2xyĵ over the box bounded by planes x=0, x=a, y=0, y=b