# NSolveODE Command ##### Command Categories (All commands)

NSolveODE( <List of Derivatives>, <Initial x-coordinate>, <List of Initial y-coordinates>, <Final x-coordinate> )
Solves (numerically) the system of differential equations
Example:
`f'(t, f, g, h) = g `
`g'(t, f, g, h) = h`
`h'(t, f, g, h) = -t h + 3t g + 2f + t`
`NSolveODE({f', g', h'}, 0, {1,2,-2}, 10)`
`NSolveODE({f', g', h'}, 0, {1,2,-2}, -5)` (solves the system backwards in time).
Example:
`x1'(t, x1, x2, x3, x4) = x2`
`x2'(t, x1, x2, x3, x4) = x3`
`x3'(t, x1, x2, x3, x4) = x4`
`x4'(t, x1, x2, x3, x4) = -8x1 + sin(t) x2 - 3x3 + t^2`
`x10 = -0.4`
`x20 = -0.3`
`x30 = 1.8`
`x40 = -1.5`
`NSolveODE({x1', x2', x3', x4'}, 0, {x10, x20, x30, x40}, 20)`
Example:
Pendulum:
`g = 9.8`
`l = 2`
`a = 5` (starting location)
`b = 3` (starting force)
`y1'(t, y1, y2) = y2`
`y2'(t, y1, y2) = (-g) / l sin(y1) `
`NSolveODE({y1', y2'}, 0, {a, b}, 20) `
`len = Length(numericalIntegral1) `
`c = Slider(0, 1, 1 / len, 1, 100, false, true, true, false) `
`x1 = l sin(y(Point(numericalIntegral1, c))) `
`y1 = -l cos(y(Point(numericalIntegral1, c))) `
`A = (x1, y1) `
`Segment((0, 0), A)`
`StartAnimation()`

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