dy/dx + x sin2y = x^3 cos^2 y
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Do you want to find dy/dx for x sin 2y = x³ cos² y ?
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x sin 2y = x³ cos² y
differentiate wrt x both sides
sin 2y + 2x cos2y dy/dx = 3x² cos²y - 2x³ cosysiny dy/dx
dy/dx ( 2xcos2y + 2x³cosysiny) = 3x² cos²y - sin2y
dy/dx = 3x² cos²y - sin2y / 2xcos2y + 2x³cosysiny
hope this helps.
differentiate wrt x both sides
sin 2y + 2x cos2y dy/dx = 3x² cos²y - 2x³ cosysiny dy/dx
dy/dx ( 2xcos2y + 2x³cosysiny) = 3x² cos²y - sin2y
dy/dx = 3x² cos²y - sin2y / 2xcos2y + 2x³cosysiny
hope this helps.
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