Standard +0.3 This is a straightforward integrating factor question with standard linear form. Part (a) requires routine application of the integrating factor method (multiply by e^{-0.1t}), and part (b) is simple substitution using the initial condition. The context is superficial and adds no mathematical complexity. Slightly above average difficulty only because it's Further Maths content, but this is one of the most mechanical topics in FP2.
5. (a) Obtain the general solution of the differential equation
$$\frac { \mathrm { d } S } { \mathrm {~d} t } - 0.1 S = t$$
(b) The differential equation in part (a) is used to model the assets, \(\pounds S\) million, of a bank \(t\) years after it was set up. Given that the initial assets of the bank were \(\pounds 200\) million, use your answer to part (a) to estimate, to the nearest \(\pounds\) million, the assets of the bank 10 years after it was set up.
5. (a) Obtain the general solution of the differential equation
$$\frac { \mathrm { d } S } { \mathrm {~d} t } - 0.1 S = t$$
(b) The differential equation in part (a) is used to model the assets, $\pounds S$ million, of a bank $t$ years after it was set up. Given that the initial assets of the bank were $\pounds 200$ million, use your answer to part (a) to estimate, to the nearest $\pounds$ million, the assets of the bank 10 years after it was set up.\\
\hfill \mbox{\textit{Edexcel FP2 Q5 [10]}}