$x_{n}$

$x_{test}$

$x_{n}$

$x_{0}$

$y'(x)=$

Zurücksetzen

⇐

⇒

Lösung anzeigen

$x_{n+1}$

$x_{n+1}$

Euler-Schritte anzeigen

f'(x, y) = ((-x) * y)
X_{i} = (-1.0046433199012035, 1.0042374315076994)
f_{i}: f'(X_{i})
h = 0.5 (slider from 0.01 to 1.5, step 0.01)
y_{nexteuler}(x, y) = y + (h * f'(x, y))
X_{tempnext}: (x(X_{i}) + h, y_{nexteuler}(X_{i}))
f_{temp}: f'(X_{tempnext})
f_{average} = mean(f_{i}, f_{temp})
y_{next}(x, y) = y + (h * f_{average})
X_{euleri} = (-1.0046433199012035, 1.0042374315076994)
L_{eulersteps}: {}
X_{0} = (-1.0046433199012035, 1.0042374315076994)
f_{euleri}: f'(X_{euleri})
richtungsfeld = SlopeField(f')
n = 0 (slider from 0 to 3000, step 1)
Eingabefeld1 = Textfield(f')
textStep: "\text{Schritt }\textcolor{#3333CC}{" + (LaTeX[n]) + "}"
dx_{euler}: 0.1 / sqrt(1 + f_{euleri}^(2))
showFunction = false
X_{next}: (x(X_{i}) + h, y_{next}(X_{i}))
S_{next} = Segment(X_{i}, X_{next})
L_{euler} = Union(L_{eulersteps}, {X_{euleri}})
lines_{euler} = PolyLine(L_{euler})
X_{nexteuler}: (x(X_{euleri}) + h, y_{nexteuler}(X_{euleri}))
L_{steps}: {}
showEuler = false
S_{nexteuler} = Segment(X_{euleri}, X_{nexteuler})
L = Union(L_{steps}, {X_{i}})
dx: 0.15 / sqrt(1 + f_{i}^(2))
S_{euler} = Segment(X_{euleri} - (dx_{euler}, (dx_{euler} * f_{euleri})), X_{euleri} + (dx_{euler}, (dx_{euler} * f_{euleri})))
S = Segment(X_{i} - (dx, (dx * f_{i})), X_{i} + (dx, (dx * f_{i})))
dx_{temp}: 0.15 / sqrt(1 + f_{temp}^(2))
S_{temp} = Segment(X_{tempnext} - (dx_{temp}, (dx_{temp} * f_{temp})), X_{tempnext} + (dx_{temp}, (dx_{temp} * f_{temp})))
lines = PolyLine(L)
S_{nexttemp} = Segment(X_{i}, X_{tempnext})
dx_{2}: 0.15 / sqrt(1 + f_{average}^(2))
S_{2} = Segment(X_{i} - (dx_{2}, (dx_{2} * f_{average})), X_{i} + (dx_{2}, (dx_{2} * f_{average})))
textAverage: "\text{Mittlere Steigung: }" + (LaTeX[f_{average}]) + ""
textTest: "\text{Steigung bei }\textcolor{#333333}{x_{test}}\text{: }" + (LaTeX[f_{temp}]) + ""
f_1 = SolveODE(f', x(X_{0}), y(X_{0}), x(Corner[1]), 0.1)
f_2 = SolveODE(f', x(X_{0}), y(X_{0}), x(Corner[2]), 0.1)
textN: "\text{Steigung bei }\textcolor{#0033CC}{x_n}\text{: }" + (LaTeX[f_{i}]) + ""