<p>It is given that&nbsp;$y=\tan 3x$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that&nbsp;$\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}=Ay\frac{\mathrm{d}y}{\mathrm{d}x}$, where&nbsp;$A$ is a constant to be determined.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Hence show that&nbsp;$\frac{{{\mathrm{d}}^{4}}y}{\mathrm{d}{{x}^{4}}}=B\frac{\mathrm{d}y}{\mathrm{d}x}\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}+Cy\frac{{{\mathrm{d}}^{3}}y}{\mathrm{d}{{x}^{3}}}$, where&nbsp;$B$ and $C$ are constants to be determined.<span class="inline-marks">[3]</span></div></li></ol>

Show that $\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}=Ay\frac{\mathrm{d}y}{\mathrm{d}x}$, where $A$ is a constant to be determined.

Hence show that $\frac{{{\mathrm{d}}^{4}}y}{\mathrm{d}{{x}^{4}}}=B\frac{\mathrm{d}y}{\mathrm{d}x}\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}+Cy\frac{{{\mathrm{d}}^{3}}y}{\mathrm{d}{{x}^{3}}}$, where $B$ and $C$ are constants to be determined.

2024 ASRJC Promo Q2

2024 ASRJC Promo Q2

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