Q. 355.0( 2 Votes )

Solve the differential equation given that when x = 2, y = 1.

Answer :

Given and when x = 2, y = 1







This is a first order linear differential equation of the form



Here, and Q = 2y


The integrating factor (I.F) of this differential equation is,





We have



[ m log a = log am]


I.F = y–1 [ elog x = x]


Hence, the solution of the differential equation is,






We know


xy–1 = 2y + c


xy–1 × y = (2y + c)y


x = (2y + c)y


However, when x = 2, we have y = 1.


2 = (2 × 1 + c) × 1


2 = 2 + c


c = 2 – 2 = 0


By substituting the value of c in the equation for x, we get


x = (2y + 0)y


x = (2y)y


x = 2y2


Thus, the solution of the given differential equation is x = 2y2


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