| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/1 (Pre-U Further Mathematics Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 8 |
| Topic | First order differential equations (integrating factor) |
| Type | Standard linear first order - variable coefficients |
| Difficulty | Standard +0.8 This is a first-order linear ODE requiring an integrating factor (sech x), followed by integration involving hyperbolic functions and application of an initial condition. While the method is standard for Further Maths students, the hyperbolic function manipulation and integration (particularly recognizing ∫sech x dx = arctan(sinh x)) requires solid technique and is more demanding than routine A-level questions, placing it moderately above average difficulty. |
| Spec | 4.07a Hyperbolic definitions: sinh, cosh, tanh as exponentials4.10c Integrating factor: first order equations |
Find, in the form $y = f(x)$, the solution of the differential equation $\frac{dy}{dx} + y\tanh x = 2\cosh x$, given that $y = \frac{3}{4}$ when $x = \ln 2$. [8]
\hfill \mbox{\textit{Pre-U Pre-U 9795/1 2018 Q5 [8]}}