EXERCISE 10.5

EXERCISE . . If F is the constant force generated by the motor of an automobile of mass M , its velocity V is given by M dV dt kV , where k is a constant. Express V in terms of t given that V = when t = . . The velocity v , of a parachute falling vertically satisfies the equation v dv g v k where g and k are constants. If v and x are both initially zero, find v in terms of x . . Find the equation of the curve whose slope is y and which passes through the point ) . . Solve the following differential equations : (i) dy (ii) ydx x dy tan (iii) sin ( ) = (iv) dy x e x y - - (v) e x dy (vi) ydx xdy ny dx  = cot (vii) dy (viii) x y dy (ix) tan y dy ) + (x) dy tan