<p>Consider the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x} + y \tan x = 2 \cos^4 x\) given that&nbsp;\(y = 1\) when&nbsp;\(x = 0\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Solve the differential equation, giving your answer in the form \(y = \mathrm{f}(x)\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Using differentiation, show that&nbsp;\(\frac{\mathrm{d}^2y}{\mathrm{d}x^2} + y = -10 \sin x \cos^3 x\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence find the first \(4\) terms of the Maclaurin series for&nbsp;\(y\).</span></div></li></ol>

Consider the differential equation \(\frac{\mathrm{d}y}{\mathrm{d}x} + y \tan x = 2 \cos^4 x\) given that \(y = 1\) when \(x = 0\).

Solve the differential equation, giving your answer in the form \(y = \mathrm{f}(x)\).

Using differentiation, show that \(\frac{\mathrm{d}^2y}{\mathrm{d}x^2} + y = -10 \sin x \cos^3 x\).

Hence find the first \(4\) terms of the Maclaurin series for \(y\).

Maclaurin Series and Power Series - General

Maclaurin Series and Power Series

International Baccalaureate Higher Level Mathematics

Solution of Differential Equations using Maclaurin's series

Solution of Differential Equations using Maclaurin's series