Q22 of 26 Page 1

Solve the differential equation :

(tan-1y – x)dy = (1 + y2)dx.


OR


Find the particular solution of the differential equation given that y = 1, when x = 0.

We have, (tan-1y – x)dy = (1 + y2)dx





It is a linear differential equation of the form


Where,



Now,



Using: , we get



Putting








OR


We have, (i)


Which is a homogeneous differential equation.


Putting y=vx and in (i), we get







Integrating both sides, we get





Substituting , we get



Given that, y=1 when x=0


From (ii), we get





⇒ x2 = 2y2 log|y| is the solution of the given equation.


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