4. (a) Find the series solution of the following differential equation about r= 0 [4] (...

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4. (a) Find the series solution of the following differential equation about r= 0 [4] ( - 1)y" + ry - y = 0. (b) Consider the differential equation [5] ry" + (r + p)y/ + (p+ 1)y = 0, where pis not an integer. Show that r = 0 is a regular singular point of the above differential equation. Obtain two linearly independent solutions about r = 0 of the given differential equation. %3D **** 4. (a) Find the series solution of the following differential equation about r= 0 [4] ( - 1)y" + ry - y = 0. (b) Consider the differential equation [5] ry" + (r + p)y/ + (p+ 1)y = 0, where pis not an integer. Show that r = 0 is a regular singular point of the above differential equation. Obtain two linearly independent solutions about r = 0 of the given differential equation. %3D ****