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Differential equations — separable and integrating factor (IB Math AA HL)
Updated October 2026
Quick answer: Separate the variables when dy/dx = f(x)g(y); substitute y = vx when dy/dx is a function of y/x; and for dy/dx + P(x)y = Q(x), multiply through by the integrating factor e^(∫P(x) dx).
HL AA covers first-order separable DEs and linear DEs solved by integrating factor. Paper 3 often layers a Maclaurin series check on top.
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5 quick questions on separable differential equations. No sign-in needed.
\(\frac{dy}{dx} = 2xy\) and \(y = 3\) when \(x = 0\). Find \(y\) when \(x = 1\).
To solve \(\frac{dy}{dx} + 3\,y = e^{x}\) (\(x \gt 0\)), you multiply both sides by an integrating factor \(\mu(x)\). Which one?
Starting from the point \((1,\ 4)\) on a solution of \(\frac{dy}{dx} = 3x - y\), take two Euler steps of size \(0.2\). What estimate of \(y(1.4)\) do you get?
\(\frac{dy}{dx} = \frac{x}{y}\), \(y > 0\), and \(y = 3\) when \(x = 0\). Find \(y\) when \(x = 4\).
To solve \(\frac{dy}{dx} + \tan{\left(x \right)}\,y = \cos{\left(x \right)}\) (\(0 \lt x \lt \frac{\pi}{2}\)), you multiply both sides by an integrating factor \(\mu(x)\). Which one?