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 = eintegral (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).
MD
Answered by Mark D. • Further Mathematics tutor
7321 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸What are polar coordinates?
a) Show that d/dx(arcsin x) = 1/(√ (1-x²)). b) Hence, use a suitable trigonometric substitution to find ∫ (1/(√ (4-2x-x²))) dx.
Let I(n) = integral from 1 to e of (ln(x)^n)/(x^2) dx where n is a natural number. Firstly find I(0). Show that I(n) = -(1/e) + n*I(n-1). Using this formula find I(1).
How do you calculate the derivative of cos inverse x?