Suppose thatv(t)

is the velocity of a falling body depending on timet

. The following differential equation

Suppose that VU) IS the VEIOCIIy 01' a talllng DOCly depending on time t. I he tollowrng ditterentlal equation dv _ = _ kv, dt 5' (where k and g are constants) can be solved using an integrating factor. To do this, rearrange equation (1) into the shape dv +h= dt g Then multiply both sides of this equation by the integrating factor e f kdt = ekt Note that the constant of integration is typically omitted in this step. This results in an equivalent differential equation: dv kt_ kt (3+kv)e ge Equation (3) can be rewritten in the form aver) = le. (you can check this, by using the product rule on the left hand side). Integrating with respect to twe get: for some constant C, and so the solution to equation (1) is v=h1