If we integrate equation (4.7), we will get the constants of integration which are found from initial condition of the fluid particle. Hence the solution of (4.7) gives the relations derived for Lagrange.
and x = x (x0, y0, z0, t)
Y = Y (x0, z0‘ z0, t)
z = z (x0, y0, z0, t).
But the solution of the 3 sets of simultaneous differential equation is very difficult to reach to Lagrangian equations from Euler’s equation.
Thus the Eulerian method is commonly used in fluid mechanics. Hence in this book if anything is not mentioned, it is the Eulerian method which is in use.