(i) If `u=x^2y++y^2z+z^2x`, show that `frac{lambdau}{lambdax}+frac{lambdau}{lambday}+frac{lambdau}{lambdaz}=(x+y+z)^2`

If z(x+y)= x^2 +y^2 show that (frac{delz}{delx}-frac{del z}{del y})^2 = 4 (1- frac{delz}{delx}+frac{delz}{dely})

x frac{dy}{dx} = y - xcos^2 frac{y}{x}

The system of homogeneous equation lambdax+(lambda+1)y +(lambda-1)z=0, (lambda+1)x+lambday+(lambda+2)z=0, (lambda-1)x+(lambda+2)y + lambdaz=0 has non-trivial solution for :

If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

A system of equations lambdax +y +z =1,x+lambday+z=lambda, x + y + lambdaz = lambda^2 have no solution then value of lambda is

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

If u=(x^(2)+y^(2)+z^(2))^(-1/2) show that x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z)=-u

If u=(x^(2)+y^(2)+z^(2))^(-1/2) show that x(del u)/(del x)+y(del u)/(del y)+z(del u)/(del z)=-u

dy/dx = frac{2x+y}{x}

The number of real values of for which the system of linear equations 2x+4y- lambdaz =0 , 4x+lambday +2z=0 , lambdax + 2y+2z=0 has infinitely many solutions , is :