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

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,

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