Mark the correct alternative in each of the following:
The solution of the differential equation x dx + y dy = x2y dy – y2 x dx, is
x dx + y dy = x2y dy – y2 x dx
⇒ x dx + y2 x dx = x2y dy – y dy
⇒ x dx(1 + y2) = y dy(x2 – 1)
By Variable separable
Integrating both sides we get
-- (1)
Put x2 – 1 = t and Put 1 + y2 = u
Diff w.r.t x Diff w.r.t y
2x dx = dt 2y dy = du
Putting values in (1) we get,
∵ log a + log b = log ab
Putting values of t and u we get,
⇒ x2 – 1 = C (1 + y2) = (A)