solve the given differential equation by using anappropriate substitution ( Each Problem is Homogeneous )  Please give a detailed explanation for everystep  (x-y)dx +x dy =0

A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance measured along the beam; [x]=[L] y = displacement of the beam; [y]=[L] = circular frequency of vibration; []=[T1] = mass of the beam per unit length; []=[ML1] D = bending rigidity of beam; [D]=[FL2] Show that the equation is dimensionally homogeneous. Note that [F]=[MLT2] see Eq. (1.21:).

Use numerical integration to compute the product of inertia of the region show with respect to the x- and y-axes.

A differential equation is d2ydt2=Ay2+Byt where y represents a distance and t is time. Determine the dimensions of constants A and B for which the equation will be dimensionally homogeneous.