Q. 37 I5.0( 2 Votes )

Solve each of the following initial value problems:

,

Answer :

,


Given and





This is a first order linear differential equation of the form



Here, and


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




We have



I.F = x [ elog x = x]


Hence, the solution of the differential equation is,







Recall





xy = x sin x + c




However, when, we have y = 1





c = 0


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



y = sin x


Thus, the solution of the given initial value problem is y = sin x


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