" 33."x(d^(2)y)/(dx^(2))+(dy)/(dx)+x=0

y = log x + c is a solution of the differential equation x(d^(2)y)/(dx^(2)) + (dy)/(dx) = 0

y = Ae^(x) + Be^(-2x) is a solution of the D.E. (d^(2)y)/(dx^(2) )+ (dy)/(dx) -2y = 0

If y=a+(b)/(x) ; prove that x(d^(2)y)/(dx^(2))+2(dy)/(dx)=0

If y=log (x + sqrt(x^(2) + 1)) then show that, (x^(2) + 1) (d^(2)y)/(dx^(2)) + x (dy)/(dx)= 0

[" The differential equation of the family of curves "],[y=c_(1)x^(3)+(c_(2))/(x)" where "c_(1)" and "c_(2)" are arbitrary "],[" constants,is "],[" O "x^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)+3y=0],[" (x) "(d^(2)y)/(dx^(2))+x(dy)/(dx)-3y=0],[" (x) "(d^(2)y)/(dx^(2))-x(dy)/(dx)+3y=0]

If y= cot x, prove that (d^(2)y)/(dx^(2)) + 2y (dy)/(dx)= 0.

The order of the differential equation 2x^(2) (d^(2)y)/(dx^(2))-3(dy)/(dx) + y = 0 is