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STEP Support Programme

STEP 3 2007 Q8 (spoilers)

I have obtained a(x) and b(x) but had to do two substitutions v = u/x and t = v'(x) to get the answer. However the mark scheme (integral) states a more efficient argument that since the equation is linear in u and it's derivatives the general solution is
u = Ax + Be^(-x) which I don't understand!

any help would be much appreciated

Hi I found out about how to use the results to find a general form of the DE.

Is it possible for a question to require you to find a suitable substitution for a homogenous equation with variable coefficients?

Sorry for the delay in replying to this!

I take it from your second comment that you have found out about the Principle of Superposition".

To answer your second question, it is possible but you are likely to be pointed in the correct direction (sort of like the second part of this question).