Solve the following differential equations:
(1 + x2)dy = (xy)dx
Now separating variable x on one side and variable y on other side, we have
Integrating both sides
Using identities:
and for RHS assuming x2 = t (substitution property) and differentiating both sides
Now, 2xdx = dt
Substituting the above value in the integral and replacing x2 with t and integrating both sides
Now replacing t by x2
Taking anti - log both sides
y2 = 1+x2