Edexcel A-Level Mathematics A2 P4.6.4 Analytical Solution of Simple First Questions

Practise Edexcel IAL P4.6.4 separable differential equations: separate and integrate, apply initial conditions, and solve for model values.

Exam points

Separate variables and integrate both sides of the first-order equation
Use an initial value to determine the integration constant and particular model
Solve the model for a requested time, value or long-term limit with units

[Maximum number: 4]

Solve the differential equation (II) to determine v as a function of x

$\frac{1}{v^{2}} \frac{\mathrm{~d} v}{\mathrm{~d} x}=-2 x \Rightarrow \int v^{-2} \mathrm{~d} v=-2 \int x \mathrm{~d} x$ $\Rightarrow \frac{v^{-1}}{-1}=-2 \frac{x^{2}}{2}(+c)$ $\Rightarrow \frac{1}{v}=x^{2}+c$ $\Rightarrow v=\frac{1}{x^{2}+c}$
(4)

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Edexcel A-Level Mathematics A2 P4.6.4 Analytical Solution of Simple First Questions question 1