Standard +0.3 This is a standard integrating factor question with a straightforward structure: the integrating factor is immediately recognizable as e^(ln(x^4+5)) = x^4+5, and the right-hand side integrates cleanly. While it requires multiple steps (identify method, find integrating factor, integrate both sides, apply initial condition), each step follows a well-practiced algorithm with no conceptual surprises. Slightly easier than average due to the clean algebraic form throughout.
Find the solution of the differential equation
$$\frac{dy}{dx} + \frac{4x^3y}{x^4 + 5} = 6x$$
for which \(y = 1\) when \(x = 1\). Give your answer in the form \(y = f(x)\). [7]
Find the solution of the differential equation
$$\frac{dy}{dx} + \frac{4x^3y}{x^4 + 5} = 6x$$
for which $y = 1$ when $x = 1$. Give your answer in the form $y = f(x)$. [7]
\hfill \mbox{\textit{CAIE Further Paper 2 2021 Q2 [7]}}