Q. 12

For each of the differential equations in question, find a particular solution satisfying the given condition:

x(x2 – 1) dy/dx = 1; y = 0 when x = 0

Answer :


Separating variables,



Or,



Integrating both sides,



Now let,




Or



Now comparing the values of A,B,C


A + B + C = 0


B-C = 0


A = -1


Solving these we will get that


Now putting the values of A,B,C in ii)



Now integrating it,





Now we are given that




Or,





Now putting the value of


Then,




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