Chapter 13 Multiple choice questions

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. Which of the following differential equations is not linear?

dy/dx – y² = 0 correct incorrect

dy/dx + sin(x) y = 0 correct incorrect

d²y/dx² + 3 dy/dx + 2y = 0 correct incorrect

x² d²y/dx² + x dy/dx – y = 0 correct incorrect

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. Which of the following is not true about linear differential equations?

A solution multiplied by a constant is also a solution. correct incorrect

The sum of solutions is also a solution. correct incorrect

A small change in the boundary conditions can lead to drastically different behaviour of the solutions. correct incorrect

The solutions do not display chaotic behaviour. correct incorrect

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. What is the integrating factor for x dy/dx– y = x² ?

e^-x correct incorrect

x^-1 correct incorrect

x^-2 correct incorrect

x³ / 3 correct incorrect

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. How would you describe the solution of d²y/dx² + 2 dy/dx + 3y = 0 ?

Decaying oscillation. correct incorrect

Critically damped oscillation. correct incorrect

Sum of decaying solutions (no oscillations). correct incorrect

None of the above. correct incorrect

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. For the second-order differential equation obeyed by a driven damped harmonic oscillator, which of the following is not related to the other three.

The complementary function. correct incorrect

The particular integral. correct incorrect

The steady-state solution. correct incorrect

The long-term behaviour. correct incorrect