(Solved): 8.1 Sketch a family of curves represented by each of the following differential equations: dy dx = ...

8.1 Sketch a family of curves represented by each of the following differential equations: dy dx = 2x + 3 and determine the equation of one of these curves which passes through the point (1, 3) 8.2 An object is thrown vertically upwards with an initial velocity u of 20m/s. The motion of the object follows the differential equation ds = u - gt dt where s is the height of the object in metres at time t seconds and g = 9.8m/s² Determine the height of the object 8.3 The current in an electric circuit is given by the equation di Ri+ L = 0 dt where L and R are constants. Show that i = le ¹ given that i =I when t =0 8.4 Solve the differential equation: dy 2x = x+3y dx given that when x = 1, y=1 8.5 In an alternating current circuit containing resistance R and inductance L the current di Ri+ L= E sin cot dt Given i=0 when t=0, show that the solution of the equation is given by: Eo E@L i-(R²0 +2²) (R$ = (R sin ot - L cos cot) + + R² +6²I² = e Z