part (a)

use the substitution u = (y-x) to find the general family of solutions of the differential equation:

dy/dx = sin(y-x)

part (b)

show that if a new independant variable is defined by y = z^(1-n) then the differential equation:

dz/dx + p(x)z = q(x)z^n where (n not equal to 1)

becomes a linear differential equation in y(x)

part (c)

use part (b) to solve the initial value problem

xz dz/dx = x^2 + 3z^2 where z(1) = 1