Q30 of 462 Page 22

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)

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