Define probale and normal law of errors,?

Question

Also give physical significance of precision constant h ?

Solve this differential eqn using method of variation of parameters

(x^2D^2 - 2xD + 2)y=6/x

Answer 1

You are asking three different questions (for the price of one). The first two questions are not well enough defined to be answered. I have not heard of the "normal law of errors" or the "precision constant h" and neither has Wikipedia. Perhaps they are mentioned in your textbook.

The differential equation can be solved by making the substitution t=log(x) and you get the homogeneous solution

y = Aexp(t) + Bexp(2t) = Ax + Bx^2

where A and B are constants. To get the particular integral by variation of parameters, let A and B be functions of x and substitute this y into the differential equation and solve for A(x) and B(x). Or, by inspection, let y=C/x and you find that C=1 from the differential equation. Then the general solution is

y = Ax + Bx^2 + 1/x