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Differential Equations

Quick questions on Particular integrals and complementary functions explained: H2 Further Mathematics

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is trial clashing with ycy_c unnoticed?
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If the trial appears in the complementary function, multiply by xx; otherwise the substitution collapses to 0=f(x)0 = \mathrm{f}(x).
What is wrong polynomial degree?
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Match the trial polynomial's degree to the forcing; a constant forcing still needs a constant trial, but a clash with a zero root may force an extra xx.
What is q1?
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State the structure of the general solution of a non-homogeneous linear ODE. [1 mark]
What is q2?
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What trial particular integral suits forcing f(x)=5e3x\mathrm{f}(x) = 5\mathrm{e}^{3x} (not in the complementary function)? [1 mark]
What is q3?
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Why must the trial be multiplied by xx when it matches the complementary function? [2 marks]

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