<ol class="abc-list"><li><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">It is given that&nbsp;\(2xy - x^2 \frac{\mathrm{d}y}{\mathrm{d}x} = 2x^4 + y^2\). Using the substitution \(wy = x^2\), show that the differential equation can be transformed to \(\frac{\mathrm{d}w}{\mathrm{d}x} = 1 + 2w^2\).</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence, solve the differential equation \(2xy - x^2 \frac{\mathrm{d}y}{\mathrm{d}x} = 2x^4 + y^2\).</span><span class="inline-marks">[3]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">It is given that&nbsp;\(u\) satisfies \(\frac{\mathrm{d}^2u}{\mathrm{d}x^2} = e^{2x}\) and has a stationary value of \(\frac{e^2}{4}\) when&nbsp;\(x = 1\). Find \(u\) in terms of \(x\).</span><span class="inline-marks">[3]</span></div></li></ol>

It is given that \(2xy - x^2 \frac{\mathrm{d}y}{\mathrm{d}x} = 2x^4 + y^2\). Using the substitution \(wy = x^2\), show that the differential equation can be transformed to \(\frac{\mathrm{d}w}{\mathrm{d}x} = 1 + 2w^2\).

Hence, solve the differential equation \(2xy - x^2 \frac{\mathrm{d}y}{\mathrm{d}x} = 2x^4 + y^2\).

It is given that \(u\) satisfies \(\frac{\mathrm{d}^2u}{\mathrm{d}x^2} = e^{2x}\) and has a stationary value of \(\frac{e^2}{4}\) when \(x = 1\). Find \(u\) in terms of \(x\).

2024 EJC P1 Q5

2024 EJC P1 Q5

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