Yes, any one of the three can be \”f(x)\”, but don\’t forget to change u1(x), u2(x), u3(x) accordingly when you switch f, g, h.

Have attached the detailed derivation of v3. Please check.

Hi,

Good question. Notice a trivial solution for the ODE (2-x) d3v/dx3 + (3-x) d2v/dx2 = 0 is d2v/dx2 = 0, which would give v1 and v2. For the third one, you can regard d2v/dx2 as a new function w(x) and it becomes a simple first-order ODE regarding w(x). Solve w(x) and then integrate it twice, and you will get v3.

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