Solve the following differential equations:

Question

Philoid · Accepted Answer

Now separating variable x on one side and variable y on another side, we have

Re - writing the equation as

Now assuming 1+y² = t²

Differentiating both sides, we get

ydy = tdt

Similarly, for LHS assuming 1+x² = v²

differentiating both sides

xdx = vdv

substituting these values in the differential equation

Integrating both sides

Re - writing as

Using identity:

and

Integrating both sides, we get

Substituting the value of v and t in the above equation