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If \sin\!\left(\dfracyx\right)=\log_e|x|+\dfracα2 is the solution of the differential equation x\cos\!\left(\dfracyx\right)\dfracdydx=y\cos\!\left(\dfracyx\right)+x and y(1)=\dfracπ3, then α^2 is equal to: | Watch the step-by-step video solution for this NIMCET PYQ.