Separable variables

Questions where the differential equation can be solved by separating variables (writing as f(y)dy = g(x)dx) and integrating both sides, without requiring an integrating factor.

53 questions · Standard +0.3

1.08k Separable differential equations: dy/dx = f(x)g(y)
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OCR Further Pure Core 2 2019 June Q5
11 marks Standard +0.8
5
2
4 \end{array} \right) + \mu \left( \begin{array} { r } 1
- 2
1 \end{array} \right) $$ Find, in exact form, the distance between \(l _ { 1 }\) and \(l _ { 2 }\).
OCR Further Additional Pure 2018 September Q3
11 marks Standard +0.8
The function \(w = f(x, y, z)\) is given by \(f(x, y, z) = x^2yz + 2xy^2z + 3xyz^2 - 24xyz\), for \(x, y, z \neq 0\).
    1. Find
    2. Hence find the values of \(a\), \(b\), \(c\) and \(d\) for which \(w\) has a stationary value when \(d = f(a, b, c)\). [5]
  2. You are given that this stationary value is a local minimum of \(w\). Find values of \(x\), \(y\) and \(z\) which show that it is not a global minimum of \(w\). [2]
Pre-U Pre-U 9794/1 2011 June Q12
10 marks Moderate -0.8
Find the general solution of the differential equation $$\frac{dy}{dx} = \frac{x}{x(1 + x^2)}$$ giving your answer in the form \(y = f(x)\). [10]