Solve the following differential equations:
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