(1)(a) Define which differential equations are called linear and nonlinear? (b) Determine which of the following equations is linear and which is nonlinear; give reasons: dx + sin x =0. dt d'x -+ In(17 +1)- dx -4 tan(t)x = cost + e' . (c) Define which systems of differential equations are called homogeneous and which are called non-homogeneous? (d) Determine which of the following systems is homogeneous and which is non- homogeneous: dx =-3cos(t)x + 5sin(t)y; dy = 2 tan(t)y +8.x. dt dx =-x+ y+sint; dt dy -=5y+6x +cost. (e) What is the general structure of solution of a linear nonhomogeneous differential equation? (f) To which kind of ordinary differential equations the principle of superposition of solutions is applicable