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Questions › DSE › DSE 2020 › Q35
4 marks, −1Mathematics › Difference and differential equations › Stability and phase diagramsHardabout 4 min

DSE 2020 Question 35: Difference and differential equations

Suppose f:R→Rf:\mathbb{R}\to\mathbb{R}f:R→R is twice differentiable, solves f′′(x)−f′(x)−f(x)−1=0f''(x)-f'(x)-f(x)-1=0f′′(x)−f′(x)−f(x)−1=0 for all xxx, and satisfies f(0)=0=f(k)f(0)=0=f(k)f(0)=0=f(k) for some k>0k>0k>0. Then

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Suppose f:ℝ→ℝ is twice differentiable, solves f′′(x)-f′(x)-f(x)-1=0 for all x, and satisfies f(0)=0=f(k) for some k>0. Then (A) f has positive and negative values over (0,k) (B) f has only positive values over (0,k) (C) f has only negative values over (0,k) (D) f=-1 on (0,k)

Also written as: Suppose f:R->R is twice differentiable, solves f''(x)-f'(x)-f(x)-1=0 for all x, and satisfies f(0)=0=f(k) for some k>0. Then

Difference and differential equations has come up 20 times in 5 exams since 2014.

What this question tests

This question is on Stability and phase diagrams, part of Difference and differential equations in Mathematics.

Whether solutions settle to an equilibrium and how to read the phase line.

TestStop has 8 past-paper questions on this subtopic.

Practise Difference and differential equationsMore on Stability and phase diagrams

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Question from the DSE 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.