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 (x⁴ y) = 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).