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,


Integrating both sides,

Now let,


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


Now putting the value of


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