Moderate -0.3 This is a straightforward application of the integrating factor method with a simple exponential function. While it's Further Maths content, the question requires only direct application of a standard technique with no problem-solving insight needed. The integration steps are routine and the initial condition application is mechanical, making it slightly easier than average overall.
Use the integrating factor method to find the solution of the differential equation
$$\frac{\text{d}y}{\text{d}x} + 2y = \text{e}^{-3x}$$
for which \(y = 1\) when \(x = 0\). Express your answer in the form \(y = \text{f}(x)\). [6]
Use the integrating factor method to find the solution of the differential equation
$$\frac{\text{d}y}{\text{d}x} + 2y = \text{e}^{-3x}$$
for which $y = 1$ when $x = 0$. Express your answer in the form $y = \text{f}(x)$. [6]
\hfill \mbox{\textit{OCR FP3 2010 Q3 [6]}}