Express x⁵ in term of legendre polynomials.

Find the differential equation of all spheres whose centres lie on the Z-axis.

Form a partial differential equation by eliminating the arbitrary constants a,b,c from z = ax+by+cxy

Find a partial differential equation of all spheres of given radius.

Find the complete integral of               p+q = sin x + sin y

Expand sin x as a finite series in powers of x , with remainder in Lagrange's form. Hence find the series for sin x .

Using Maclaurin's series expand the following function in powers of x 

e^{sin x}

If xy = 4 , find the maximum and minimum value of 4x + 9y

Find the partial differential equation of eliminating f from z = xy + (x²+y²+z²)

Eliminate the arbitrary function f and g from z = f(x+iy) + g(x-iy) and form a partial differential equation.

Form partial differential equation by eliminating arbitrary function 

z =  x + y + f(xy)