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

Question

For each of the differential equations in question, find a particular solution satisfying the given condition: x(x 2 – 1) dy/dx = 1; y = 0 when x = 0

Philoid · Accepted 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,