$\Delta x = {0.69}$

Initial condition

Exact Solution

$F(x,y) =$

$n = {0}$

y_n

dx/dy

$x_n$

y_{n+1}

Euler approximation

Your differential equation:

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Exact Solution

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F(x, y) = x + y
step = 0.69 (slider from 0.01 to 2, step 0.01)
A: (-3.37, 2.48)
A2: x(A)
A3: A2 + step
A4: A3 + step
A5: A4 + step
A6: A5 + step
A7: A6 + step
A8: A7 + step
A9: A8 + step
A10: A9 + step
A11: A10 + step
A12: A11 + step
A13: A12 + step
A14: A13 + step
A15: A14 + step
A16: A15 + step
A17: A16 + step
A18: A17 + step
A19: A18 + step
A20: A19 + step
A21: A20 + step
A22: A21 + step
A23: A22 + step
A24: A23 + step
A25: A24 + step
A26: A25 + step
A27: A26 + step
A28: A27 + step
A29: A28 + step
A30: A29 + step
A31: A30 + step
A32: A31 + step
A33: A32 + step
A34: A33 + step
A35: A34 + step
A36: A35 + step
A37: A36 + step
A38: A37 + step
A39: A38 + step
A40: A39 + step
A41: A40 + step
A42: A41 + step
A43: A42 + step
A44: A43 + step
A45: A44 + step
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A47: A46 + step
A48: A47 + step
A49: A48 + step
A50: A49 + step
A51: A50 + step
A52: A51 + step
A53: A52 + step
A54: A53 + step
A55: A54 + step
A56: A55 + step
A57: A56 + step
A58: A57 + step
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A60: A59 + step
A61: A60 + step
A62: A61 + step
A63: A62 + step
A64: A63 + step
A65: A64 + step
A66: A65 + step
A67: A66 + step
A68: A67 + step
A69: A68 + step
A70: A69 + step
A71: A70 + step
A72: A71 + step
A73: A72 + step
A74: A73 + step
A75: A74 + step
A76: A75 + step
A77: A76 + step
A78: A77 + step
A79: A78 + step
A80: A79 + step
A81: A80 + step
A82: A81 + step
A83: A82 + step
A84: A83 + step
A85: A84 + step
A86: A85 + step
A87: A86 + step
A88: A87 + step
A89: A88 + step
A90: A89 + step
A91: A90 + step
A92: A91 + step
A93: A92 + step
A94: A93 + step
A95: A94 + step
A96: A95 + step
A97: A96 + step
A98: A97 + step
A99: A98 + step
B2: y(A)
C2: F(A2, B2)
D2: B2 + (step * C2)
B3: D2
C3: F(A3, B3)
D3: B3 + (step * C3)
B4: D3
C4: F(A4, B4)
D4: B4 + (step * C4)
B5: D4
C5: F(A5, B5)
D5: B5 + (step * C5)
B6: D5
C6: F(A6, B6)
D6: B6 + (step * C6)
B7: D6
C7: F(A7, B7)
D7: B7 + (step * C7)
B8: D7
C8: F(A8, B8)
D8: B8 + (step * C8)
B9: D8
C9: F(A9, B9)
D9: B9 + (step * C9)
B10: D9
C10: F(A10, B10)
D10: B10 + (step * C10)
B11: D10
C11: F(A11, B11)
D11: B11 + (step * C11)
B12: D11
C12: F(A12, B12)
D12: B12 + (step * C12)
B13: D12
C13: F(A13, B13)
D13: B13 + (step * C13)
B14: D13
C14: F(A14, B14)
D14: B14 + (step * C14)
B15: D14
C15: F(A15, B15)
D15: B15 + (step * C15)
B16: D15
C16: F(A16, B16)
D16: B16 + (step * C16)
B17: D16
C17: F(A17, B17)
D17: B17 + (step * C17)
B18: D17
C18: F(A18, B18)
D18: B18 + (step * C18)
B19: D18
C19: F(A19, B19)
D19: B19 + (step * C19)
B20: D19
C20: F(A20, B20)
D20: B20 + (step * C20)
B21: D20
C21: F(A21, B21)
D21: B21 + (step * C21)
B22: D21
C22: F(A22, B22)
D22: B22 + (step * C22)
B23: D22
C23: F(A23, B23)
D23: B23 + (step * C23)
B24: D23
C24: F(A24, B24)
D24: B24 + (step * C24)
B25: D24
C25: F(A25, B25)
D25: B25 + (step * C25)
B26: D25
C26: F(A26, B26)
D26: B26 + (step * C26)
B27: D26
C27: F(A27, B27)
D27: B27 + (step * C27)
B28: D27
C28: F(A28, B28)
D28: B28 + (step * C28)
B29: D28
C29: F(A29, B29)
D29: B29 + (step * C29)
B30: D29
C30: F(A30, B30)
D30: B30 + (step * C30)
B31: D30
C31: F(A31, B31)
D31: B31 + (step * C31)
B32: D31
C32: F(A32, B32)
D32: B32 + (step * C32)
B33: D32
C33: F(A33, B33)
D33: B33 + (step * C33)
B34: D33
C34: F(A34, B34)
D34: B34 + (step * C34)
B35: D34
C35: F(A35, B35)
D35: B35 + (step * C35)
B36: D35
C36: F(A36, B36)
D36: B36 + (step * C36)
B37: D36
C37: F(A37, B37)
D37: B37 + (step * C37)
B38: D37
C38: F(A38, B38)
D38: B38 + (step * C38)
B39: D38
C39: F(A39, B39)
D39: B39 + (step * C39)
B40: D39
C40: F(A40, B40)
D40: B40 + (step * C40)
B41: D40
C41: F(A41, B41)
D41: B41 + (step * C41)
B42: D41
C42: F(A42, B42)
D42: B42 + (step * C42)
B43: D42
C43: F(A43, B43)
D43: B43 + (step * C43)
B44: D43
C44: F(A44, B44)
D44: B44 + (step * C44)
B45: D44
C45: F(A45, B45)
D45: B45 + (step * C45)
B46: D45
C46: F(A46, B46)
D46: B46 + (step * C46)
B47: D46
C47: F(A47, B47)
D47: B47 + (step * C47)
B48: D47
C48: F(A48, B48)
D48: B48 + (step * C48)
B49: D48
C49: F(A49, B49)
D49: B49 + (step * C49)
B50: D49
C50: F(A50, B50)
D50: B50 + (step * C50)
B51: D50
C51: F(A51, B51)
D51: B51 + (step * C51)
B52: D51
C52: F(A52, B52)
D52: B52 + (step * C52)
B53: D52
C53: F(A53, B53)
D53: B53 + (step * C53)
B54: D53
C54: F(A54, B54)
D54: B54 + (step * C54)
B55: D54
C55: F(A55, B55)
D55: B55 + (step * C55)
B56: D55
C56: F(A56, B56)
D56: B56 + (step * C56)
B57: D56
C57: F(A57, B57)
D57: B57 + (step * C57)
B58: D57
C58: F(A58, B58)
D58: B58 + (step * C58)
B59: D58
C59: F(A59, B59)
D59: B59 + (step * C59)
B60: D59
C60: F(A60, B60)
D60: B60 + (step * C60)
B61: D60
C61: F(A61, B61)
D61: B61 + (step * C61)
B62: D61
C62: F(A62, B62)
D62: B62 + (step * C62)
B63: D62
C63: F(A63, B63)
D63: B63 + (step * C63)
B64: D63
C64: F(A64, B64)
D64: B64 + (step * C64)
B65: D64
C65: F(A65, B65)
D65: B65 + (step * C65)
B66: D65
C66: F(A66, B66)
D66: B66 + (step * C66)
B67: D66
C67: F(A67, B67)
D67: B67 + (step * C67)
B68: D67
C68: F(A68, B68)
D68: B68 + (step * C68)
B69: D68
C69: F(A69, B69)
D69: B69 + (step * C69)
B70: D69
C70: F(A70, B70)
D70: B70 + (step * C70)
B71: D70
C71: F(A71, B71)
D71: B71 + (step * C71)
B72: D71
C72: F(A72, B72)
D72: B72 + (step * C72)
B73: D72
C73: F(A73, B73)
D73: B73 + (step * C73)
B74: D73
C74: F(A74, B74)
D74: B74 + (step * C74)
B75: D74
C75: F(A75, B75)
D75: B75 + (step * C75)
B76: D75
C76: F(A76, B76)
D76: B76 + (step * C76)
B77: D76
C77: F(A77, B77)
D77: B77 + (step * C77)
B78: D77
C78: F(A78, B78)
D78: B78 + (step * C78)
B79: D78
C79: F(A79, B79)
D79: B79 + (step * C79)
B80: D79
C80: F(A80, B80)
D80: B80 + (step * C80)
B81: D80
C81: F(A81, B81)
D81: B81 + (step * C81)
B82: D81
C82: F(A82, B82)
D82: B82 + (step * C82)
B83: D82
C83: F(A83, B83)
D83: B83 + (step * C83)
B84: D83
C84: F(A84, B84)
D84: B84 + (step * C84)
B85: D84
C85: F(A85, B85)
D85: B85 + (step * C85)
B86: D85
C86: F(A86, B86)
D86: B86 + (step * C86)
B87: D86
C87: F(A87, B87)
D87: B87 + (step * C87)
B88: D87
C88: F(A88, B88)
D88: B88 + (step * C88)
B89: D88
C89: F(A89, B89)
D89: B89 + (step * C89)
B90: D89
C90: F(A90, B90)
D90: B90 + (step * C90)
B91: D90
C91: F(A91, B91)
D91: B91 + (step * C91)
B92: D91
C92: F(A92, B92)
D92: B92 + (step * C92)
B93: D92
C93: F(A93, B93)
D93: B93 + (step * C93)
B94: D93
C94: F(A94, B94)
D94: B94 + (step * C94)
B95: D94
C95: F(A95, B95)
D95: B95 + (step * C95)
B96: D95
C96: F(A96, B96)
D96: B96 + (step * C96)
B97: D96
C97: F(A97, B97)
D97: B97 + (step * C97)
B98: D97
C98: F(A98, B98)
D98: B98 + (step * C98)
B99: D98
C99: F(A99, B99)
PreciseSoln = SolveODE(F, x(A), y(A), 100, 0.01)
InputBox1 = Textfield(F)
text1: "$\frac{dy}{dx}=" + (LaTeX[F]) + "$ "
n: 0
A100: A99 + step
D99: B99 + (step * C99)
B100: D99
C100: F(A100, B100)
D100: B100 + (step * C100)
EulerList = PointList(Transpose[{A1:A100, B1:B100}])
Euler = PolyLine(EulerList)
ShownPoints = Sequence(Element[EulerList, i], i, 1, n)
NewEuler = PolyLine(ShownPoints)
Field = SlopeField(F, 20)
showSolution = false
EulerSegments = Sequence(Segment[Element[ShownPoints, i] - ((0.4 * step) * (cos(atand(F(Element[ShownPoints, i]))), sin(atand(F(Element[ShownPoints, i]))))), Element[ShownPoints, i] + ((0.4 * step) * (cos(atand(F(Element[ShownPoints, i]))), sin(atand(F(Element[ShownPoints, i])))))], i, 1, n)