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Report a translation problem
Ly ≡ (2x + 1)2 d
2y
dx
2
− 8(2x + 1)dy
dx
+ 24y.
(a) [8 marks] Find the general solution of the homogeneous differential equation
Ly(x) = 0.
[Hint. Show that y1(x) = (2x + 1)2
solves Ly = 0, and then seek a solution of the
form y(x) = u(x)y1(x).]
(b) [9 marks] Determine the Green’s function for the boundary value problem
Ly(x) = f(x),
y(0) = α, y(1) = β.
(c) [8 marks] Use the Green’s function obtained in (b) to write down the solution for
general data {f(x), α, β}, where f(x) is a given function, and α and β are given
real constants.
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