OCR MEI C4 — Question 7 4 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDifferential equations
TypeSeparable variables - standard (polynomial/exponential x-side)
DifficultyModerate -0.8 This is a straightforward separable variables question requiring only basic integration and substitution of initial conditions. The separation is immediate (y dy = 2x dx), integration yields standard results (y²/2 = x² + c), and finding c is trivial. This is simpler than average A-level questions as it involves minimal steps and no conceptual challenges.
Spec1.08k Separable differential equations: dy/dx = f(x)g(y)
7 Solve the differential equation \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 x } { y }\) given that when \(x = 1 , y = 2\).
Question 7:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{dy}{dx} = \frac{2x}{y}\)B1
\(\Rightarrow y\frac{dy}{dx} = 2x \Rightarrow \frac{y^2}{2} = x^2 + c\)M1A1
When \(x=1,\ y=2\), so \(c = 1\)B1
\(\Rightarrow 2 = y^2 - 2x^2\)
Total: 4 
## Question 7:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{dy}{dx} = \frac{2x}{y}$ | B1 | |
| $\Rightarrow y\frac{dy}{dx} = 2x \Rightarrow \frac{y^2}{2} = x^2 + c$ | M1A1 | |
| When $x=1,\ y=2$, so $c = 1$ | B1 | |
| $\Rightarrow 2 = y^2 - 2x^2$ | | |
| **Total: 4** | | |

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7 Solve the differential equation $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 x } { y }$ given that when $x = 1 , y = 2$.

\hfill \mbox{\textit{OCR MEI C4  Q7 [4]}}
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Q1 4 Q2 4 Q3 6 Q4 7 Q5 5 Q6 6 Q7 4 Q8 19 Q9 17