| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Differential equations |
| Type | Separable variables - standard (polynomial/exponential x-side) |
| Difficulty | Moderate -0.3 Part (i) is a routine differentiation exercise requiring only the chain rule and knowledge of basic trig derivatives. Part (ii) is a standard separable variables question with straightforward integration of trig functions, though the algebraic manipulation (recognizing sin x tan x = sin²x/cos x leads to sec x after separation) requires some care. Overall slightly easier than average due to being a textbook-style separable DE with no conceptual surprises. |
| Spec | 1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.08k Separable differential equations: dy/dx = f(x)g(y) |
(i) Show that, if $y = \operatorname { cosec } x$, then $\frac { \mathrm { d } y } { \mathrm {~d} x }$ can be expressed as $- \operatorname { cosec } x \cot x$.\\
(ii) Solve the differential equation
$$\frac { \mathrm { d } x } { \mathrm {~d} t } = - \sin x \tan x \cot t$$
given that $x = \frac { 1 } { 6 } \pi$ when $t = \frac { 1 } { 2 } \pi$.
\hfill \mbox{\textit{OCR C4 2008 Q7 [8]}}