Q25 of 29 Page 9

Solve the differential equation (x2 – y2) dx + 2xydy = 0.

OR


Find the particular solution of the differential equation , given that y = 0 when x = 1.[CBSE 2018]

(x2 – y2) dx + 2xydy = 0



As this is a homogeneous differential equation thus,


Put





Integrating both sides, we get,



⇒log x = –log (1 + v2) + log c


⇒x (1 + v2) = c



⇒x2 + y2 = cx


OR


Given:


• At x = 1, y = 0




This is in the form of first order linear differential equation hence,



Therefore, solution is


At



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23

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 24

Find the particular solution of the differential equation , given that y = π/4.

OR


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In each of the question, show that the given differential equation is homogeneous and solve each of them.

(x2 + xy)dy = (x2 + y2)dx [CBSE 2013]