| Exam Board | Edexcel |
| Module | C4 (Core Mathematics 4) |
| Year | 2007 |
| Session | January |
| Topic | Integration with Partial Fractions |
4. (a) Express \(\frac { 2 x - 1 } { ( x - 1 ) ( 2 x - 3 ) }\) in partial fractions.
(b) Given that \(x \geqslant 2\), find the general solution of the differential equation
$$( 2 x - 3 ) ( x - 1 ) \frac { \mathrm { d } y } { \mathrm {~d} x } = ( 2 x - 1 ) y$$
(c) Hence find the particular solution of this differential equation that satisfies \(y = 10\) at \(x = 2\), giving your answer in the form \(y = \mathrm { f } ( x )\).