2 Find the solution of the differential equation $$\frac { d y } { d x } + \frac { 4 x ^ { 3 } y } { x ^ { 4 } + 5 } = 6 x$$ for which \(y = 1\) when \(x = 1\). Give your answer in the form \(y = f ( x )\).
\includegraphics[max width=\textwidth, alt={}, center]{a921c01f-4d8e-47cf-9f34-d7d7bf9c9fdd-04_867_812_278_621} The diagram shows the curve with equation \(\mathrm { y } = 1 - \mathrm { x } ^ { 2 }\) for \(0 \leqslant x \leqslant 1\), together with a set of \(n\) rectangles of width \(\frac { 1 } { n }\).

1. By considering the sum of the areas of the rectangles, show that $$\int _ { 0 } ^ { 1 } \left( 1 - x ^ { 2 } \right) d x < \frac { 4 n ^ { 2 } + 3 n - 1 } { 6 n ^ { 2 } }$$
2. Use a similar method to find, in terms of \(n\), a lower bound for \(\int _ { 0 } ^ { 1 } \left( 1 - x ^ { 2 } \right) \mathrm { dx }\).