Q. 37 O4.0( 2 Votes )

Solve each of the following initial value problems:

, tan x ≠ 0 given that y = 0 when

Answer :

, tan x ≠ 0 given that y = 0 when


Given and







This is a first order linear differential equation of the form



Here, P = cot x and Q = 2x + x2 cot x


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




We have



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


Hence, the solution of the differential equation is,








Recall





y sin x = x2sin x + c




However, when, we have y = 0






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




Thus, the solution of the given initial value problem is


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