MT171 - FEEDBACK on QUESTION SHEET 10 - 2018/19 MARKING COMMENTS There are 10 marks from the questions marked, which are: Q1 (a) or (b)/ Q2(a) and (c)/ Q2(d)/ Q3 (a) or (b)/ Q4 (a), (b), (c) and (e) Each part of question will be classified as 0-if it is mostly incorrect; 1-if it is about half correct; 2-if it is mostly correct. The maximum you can get is 10 marks. For continuous assessment: if you didn't do enough work or gave in your work after the deadline, there will be a box encircling a zero at the top of page 1 of your work. Otherwise your work will have gained a 'one' and nothing will appear written. Comment 1 (C1) You need to improve the clarity of your presentation. Comment 2 (C2) Explain what you are doing. For example, state the type of differential equation that you are solving. Comment 3 (C3) Use correct notation! An equation needs to be written here. This needs a LHS (left hand side) and a RHS (right hand side)! Comment 4 (C4) Use correct mathematical language. Comment 5 (C5) The details of integrals evaluation must be given! Q1 (b) Comment 1.1 (C1.1) Before you start solving the equation, you should check the type of equation you have. For example in here you have a Bernoulli equation. Then you start your solution. Comment 1.2(C1.2) You must state that c (or any other letter you use) is an arbitrary constant. Comment 1.3(C1.3) The variable 'v' should be replaced by its expression in terms of y(x) so that the final solution y(x) is given. Comment 1.4(C1.4) The integral e® je dt 2t 2t is not an elementary function and is to be left in that form. It is what is called the Exponential Integral Ei.
Q2(a), (c) and (d) Comment 2.1(C2.1) It may be faster to complete the square than to use the quadratic form. Comment 2.2(C2.2) When the auxiliary equation has a repeated root you can assume that an independent solution is obtained when you multiply the known solution by (x), without the need to deduce it (as done in lectures to illustrate the fact). However you must state that a second linearly independent solution is obtained by multiplying by x the known solution. Comment 2.3(C2.3) You need to justify how you get the auxiliary equation: take y (x )= emx and then use the fact that emx # 0 to get the auxiliary equation. Comment 2.4(C2.4) In the case of an auxiliary equation with complex roots you should show how you obtain the real solution in terms of cos and sin from the exponential form. For example in (d), from the auxiliary equation, we get the two linearly independent solutions, which give the general solution in the form ny (* = (1+2)x, y, (x) = (1-2)x, y(x)=c,e(1+2i)x +Ce(1-2i)x ", for c1 and C2 arbitrary constants. To get the general solution in real form we use Euler's formula to get (x) = c, e*(cosRx) +isin(x