Q. 215.0( 3 Votes )

Find the particul

Answer :

Given: x = 2, y = π


To find: the particular solution of the differential equation


given:


It can be rewritten as,



Dividing throughout by x we get,




It is a homogenous differential equation,


Now let


Now differentiate this with respect to x, we get



Applying the product rule of differentiation, we get




Substituting these values in equation (i), we get








Now integrating on both sides, we get



log |cosec v-cot v|=-log |x|+C


Substituting the value of v, we get



But given x=2 when y=π, now substituting these values in above equation, we get



But , so above equation becomes



Substituting the corresponding values, we get



log |1|+log |2|=C


But log 1=0, so above equation becomes,


C=log 2


Now substituting this value in equation (ii), we get




Cancelling the log on both sides, we get



Hence this is the particular solution of the differential equation


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