(del x_(2))/(del)int(ln(1+sin^(2)x))/(cos^(2)x)dx

If u=log(x^(2)+y^(2)+z^(2)) prove that (del^(2)u)/(del x^(2))+(del^(2)u)/(del y^(2))+(del^(2)u)/(del z^(2) = 2/(x^(2)+y^(2)+z^(2)

If u =x ^(2) + y ^(2) evaluate (del^(2)f)/(del x ^(2)) + (del ^(2) f)/(dy ^(2)):

The correct Schrodinger's wave equation for an electron with total energy E and potential energy V is given by : (del^(2)Psi)/(del x^(2))+(del^(2)Psi)/(dely^(2)) +(del^(2)Psi)/(dz^(2))+(8pi^(2))/(mh^(2)) (E-V) Psi=0 ; (del^(2)Psi)/(del x^(2)) +(del^(2)Psi)/(dely^(2)) +(del^(2)Psi)/(delz^(2))+(8pim)/(h^(2))(E-V)Psi=0 ; (del^(2)Psi)/(delx^(2)) +(del^(2)Psi)/(dely^(2)) +(del^(2)Psi)/(delz^(2)) +(8pi^(2)m)/(h^(2))(E-V)Psi=0 ; (del^(2)Psi)/(delx^(2))+(del^(2)Psi)/(dely^(2))+(del^(2)Psi)/(delz^(2)) +(8pi^(2)h)/(m^(2))(E-V)Psi=0

Let w(x, y, z)=(1)/(sqrt(x^(2)+y^(2)+z^(2)))(x, y, z) != (0, 0, 0) . Show that (del^(2)w)/(delx^(2))+(del^(2)w)/(dely^(2))+(del^(2)w)/(delz^(2))=0

If u=log sqrt(x^(2) + y^(2)) , then (del^(2) u)/(del x^(2)) + (del^(2)u)/(del y^(2)) is

If V(x,y) = e^(x) (x cos y - y siny) , then prove that (del^(2)V)/(del x^(2)) + (del^(2) V)/(del y^(2)) =0

Find (del f)/(del x), (del f)/(del y),(del^(2) f)/(delx^(2)), (del^(2) f)/(del y^(2)) , at x=2, y=3 if f(x,y) =2x^(2) + 3y^(2) - 8xy .

If y=f(x+ct)+g(x-ct), then show that (del^(2)y)/(del t^(2))=c^(2)(del^(2)y)/(del x^(2))

A function f (x,y) is said to be harmonic if (del^(2)f)/(del x ^(2)) + (del^(2)f)/(dely^(2)) =

int(sin2x)/(sin^(2)x+2cos^(2)x)dx(i)-log(1+sin^(2)x)+C(ii)log(1+cos^(2)x)+C( iii) -log(1+cos^(2)x)+C(iv)log(1+tan^(2)x)+C