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If y=y(x),\; x\in(0,π/2) be the solution curve of the differential equation (\sin^22x)\dfracdydx+(8\sin^22x+2\sin 4x)y=2e^-4x(2\sin 2x+\cos 2x), with y(π/4)=e^-π, then y(π/6) is equal to : | Watch the step-by-step video solution for this NIMCET PYQ.