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By using an integrating factor, solve the differential equation dy/dx + 4y/x = 6x^-3 (6 marks)

Answer : y = 3/x²+ c/x⁴ Integrating factor is 4/x (1 mark) => I = e^{integral (4/x) dx}(1 mark) => I = x⁴(1 mark). Using the formula, d/dx (x⁴y) = 6x (1 mark)=> x⁴y = integral(6x)dx (1 mark for integrating). Rearranging gets to answer of y=3/x²+ c/x⁴. Where c is an arbitary constant (1 mark).

Answered by Mark D. • Further Mathematics tutor

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By using an integrating factor, solve the differential equation dy/dx + 4y/x = 6x^-3 (6 marks)

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