ky my2 dx Now we will try to decompose the coefficient of

Last updated: 9/12/2023

ky my2 dx Now we will try to decompose the coefficient of into partial fractions dy dx 1 A B Let y k my yk my where A and B are constants to be determined From 6 we get 1 A k my By which gives 1 Ak and 1 or A Hence and B 1 y k my ky Bk m m 1 k k my Thus the given differential equation can be rewritten as 1 1 m dy 1 ky kk my or For the case under consideration Eqn 7 can be expressed as ny In k my 1 for y0 and k my 0 In the integration of Eqn 7 the signs of y and k my play an important role We now discuss the following possible cases Case 1 y 0 and k my 0 0 y k which on integrating yields 6 7 Iny In k my x C where e is a constant of integration The above equation can be further express as In y In k my x c 1 4 my exp x c Case II y 0 When y 0 then k my 0 because m 0 k 0 In this case Eqn 7 on integration can be written as