Specialist Mathematics · Unit 4 · Rates of change and differential equations · Differential equations
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Consider the differential equation \(\frac{dy}{dx} = x - 2y\). (a) Determine the equation of the isocline where the slope is zero. (1 mark) (b) Calculate the slope at the point \((3, 2)\). (1 mark) (c) Determine the coordinates of all points in the region \(-2 \leq x \leq 2\), \(-1 \leq y \leq 2\) where the slope equals \(-1\). (2 marks)
A slope field for the differential equation dy/dx = x + y is drawn. At the point (1, 2), find the gradient of the line segment shown in the slope field.
A slope field for the differential equation dy/dx = x + y is drawn. At the point (1, 2), calculate the gradient of the solution curve passing through this point.