A1.1 Solve the following problems using the techniques required in each question (i) Given that
Mt) = er
is a solution of
t y" — (1 + t)y' + y = 0, show that, by reduction of order, the general solution to this equation is y(t) = + c.2 (1 + t). (ii) Find the general solution of t y" — (1 + t) y' +y=t2e2t using variation of parameters. A1.2 (i) Consider a chemical reaction in which compounds A and 13 combine to form a third compound X. The reaction can be written as
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