DP Further Mathematics HL Questionbank
Numerical solution of \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = f\left( {x,y} \right)\) using Euler’s method.
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- 18M.2.hl.TZ0.4d: Given that all the isoclines from a slope field of a differential equation are straight lines...
- 18M.2.hl.TZ0.4c: The slope field for the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = x + y\)...
- 18M.2.hl.TZ0.4b.i: \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \) constant.
- 18M.2.hl.TZ0.4a.iii: \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = x - 1\).
- 18M.2.hl.TZ0.4a.ii: \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = x + 1\).
- 18M.2.hl.TZ0.4a.i: \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 2\).
- 18M.2.hl.TZ0.2b.ii: Show that...
- 18M.2.hl.TZ0.2b.i: Show...
- 18M.2.hl.TZ0.2a: Use Euler’s method with step length 0.1 to find an approximate value of \(y\) when \(x = 0.4\).
- 18M.1.hl.TZ0.11c: Hence show that the solution to the differential...
- 18M.1.hl.TZ0.11b: Show that the differential...
- 18M.1.hl.TZ0.11a: Show that...
- 14M.1.hl.TZ0.2: Consider the differential equation \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = {y^3} - {x^3}\) for...
- 15M.2.hl.TZ0.1a: Using Euler’s method with increments of \(0.2\), find an approximate value for \(y\) when \(x = 1\).
- 15M.2.hl.TZ0.1b: Explain how Euler’s method could be improved to provide a better approximation.
