Q. 415.0( 1 Vote )

Find the particular solution of the differential equation y ≠ 0 given that x = 0 when

Answer :

Given



This is a first order linear differential equation of the form



Here, P = cot y and Q = 2y + y2cot y


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




We have



I.F = sin y [ elog x = x]


Hence, the solution of the differential equation is,








Recall





x sin y = y2 sin y + c




x = y2 + c cosec y


However, when, we have x = 0.






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




Thus, the solution of the given differential equation is


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