Q. 155.0( 1 Vote )

Find the particular solution of the differential equation

given that when

Answer :

Given: (1 – y2)(1 + log x)dx + 2xy dy = 0


To find: a particular solution of the given differential equation


(1 – y2)(1 + log x)dx + 2xy dy = 0





Integrating both sides:



In first integral:


Put 1 + log x = t



In second integral:


Put 1 – y2 = u


2y dy = du


So,







It is given that when x = 1 the value of y = 0


Therefore,



{ log 1 = 0}





So, the solution of the differential equation is



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