Dgl-numerisch und analytisch

Heun Start bei A?

C

Lösung durch A zeigen

Sind die hellblauen Graphen Lösungen?

AgleichC = true
E = (0.9330203053582854, 0.38734260241149115)
A = (-0.20979574857309038, 0.720217836059295)
C = If(AgleichC, (x(A) + 0.25, y(A)), E)
C1: y(C)
B = (7.997135057530545, 0.3528845292527618)
w(x, y) = y^(2) - x
Steigungsfeld2 = SlopeField(w(x, y))
A1 = 0 (slider from -5 to 5)
A2 = 1 (slider from -5 to 5)
A3 = 2 (slider from -5 to 5)
A4 = 3 (slider from -5 to 5)
A5 = 4 (slider from -5 to 5)
A6 = 5 (slider from -5 to 5)
A7 = 6 (slider from -5 to 10)
A8 = 7 (slider from -5 to 10)
A9 = 8 (slider from -5 to 10)
A10 = 9 (slider from -5 to 10)
A11 = 10 (slider from -5 to 20)
A12 = 11 (slider from -5 to 20)
A13 = 12 (slider from -5 to 20)
A14 = 13 (slider from -5 to 20)
A15 = 14 (slider from -5 to 20)
A16 = 15 (slider from -5 to 20)
A17 = 16 (slider from -5 to 20)
A18 = 17 (slider from -5 to 20)
A19 = 18 (slider from -5 to 20)
A20 = 19 (slider from -5 to 20)
A21 = 20 (slider from -5 to 20)
A22 = 21 (slider from -5 to 50)
A23 = 22 (slider from -5 to 50)
A24 = 23 (slider from -5 to 50)
A25 = 24 (slider from -5 to 50)
A26 = 25 (slider from -5 to 50)
A27 = 26 (slider from -5 to 50)
A28 = 27 (slider from -5 to 50)
A29 = 28 (slider from -5 to 50)
A30 = 29 (slider from -5 to 50)
A31 = 30 (slider from -5 to 50)
A32 = 31 (slider from -5 to 50)
A33 = 32 (slider from -5 to 50)
B1: x(C)
A34 = 33
A35 = 34
A36 = 35
A37 = 36
A38 = 37
A39 = 38
A40 = 39
A41 = 40
A42 = 41
A43 = 42
A44 = 43
A45 = 44
A46 = 45
A47 = 46
A48 = 47
A49 = 48
A50 = 49
A51 = 50
A52 = 51
A53 = 52
A54 = 53
A55 = 54
A56 = 55
A57 = 56
A58 = 57
A59 = 58
A60 = 59
A61 = 60
A62 = 61
A63 = 62
A64 = 63
A65 = 64
f = SolveODE(w(x, y), x(A) + 0.25, y(A), x(B), 0.05)
F = (-2.5, -3.5)
G = (8.5, -3.5)
H = (-2.5, 3.5)
p(x) = If[x > 2 ∧ x < 8, (-sqrt(x))]
q(x) = If[x > 2 ∧ x < 8, sqrt(x)]
I = Point(xAxis)
J = (-2.146492467829537, -0.31737348675061133)
K = (-1.8375758260050536, 0.23288428149925006)
c = Vector(J, K)
L = (-1.1328597368429505, -1.2923916375091375)
M = (-0.8722113203035424, -0.7614411593733065)
d = Vector(L, M)
N = (-1.1328597368429505, 0.6856402346732587)
O = (-0.8529040301895122, 1.2745125831511808)
e = Vector(N, O)
P = (1.8597702308317343, -2.2867170783816944)
Q = (2.1590332275992026, -1.7364593101318329)
i = Vector(P, Q)
R = (4.360064300598649, -2.78870662134648)
S = (4.668980942423132, -2.267409788267664)
j = Vector(R, S)
T = (6.873083629758903, -3.3043867882103086)
U = (7.149177878389535, -2.7628173005117604)
k = Vector(T, U)
V = (0.35301175825089226, -1.7433923824909636)
W = (0.6503440260069578, -1.2549179426059984)
l = Vector(V, W)
Z = (-0.13546268163407277, 1.1980732663815434)
A_1 = (0.130012557433843, 1.2290237445173744)
m = Vector(Z, A_1)
B_1 = (1.8821491352820872, 1.760880773205525)
C_1 = (2.115767345661853, 2.2068791748396235)
s = Vector(B_1, C_1)
D_1 = (3.8785229330728135, 2.18564115571419)
E_1 = (4.122760153015296, 2.705972624287305)
t = Vector(D_1, E_1)
F_1 = (6.405847208999371, 2.7484486625381717)
G_1 = (6.650084428941853, 3.2687801311112863)
u_1 = Vector(F_1, G_1)
H_1 = Point(xAxis)
I_1 = Point(xAxis)
v_1 = Vector(H_1, I_1)
J_1 = (0.6291060068815246, 0.9963120846899274)
K_1 = (1.3299606380208222, 0.9963120846899274)
w_1 = Vector(J_1, K_1)
L_1 = (3.634285713130331, 1.9944989835852907)
M_1 = (4.313902325144196, 1.9944989835852907)
a_1 = Vector(L_1, M_1)
N_1 = (0.6715820451323912, -1.0000617131007992)
O_1 = (1.308722618895389, -1.0000617131007992)
b_1 = Vector(N_1, O_1)
P_1 = (3.687380760943914, -1.9982486119961624)
Q_1 = (4.292664306018763, -1.9982486119961624)
c_1 = Vector(P_1, Q_1)
R_1 = (1.8609111161566538, 0.3166954726760631)
S_1 = (2.1582433839127195, -0.27796906283606826)
d_1 = Vector(R_1, S_1)
T_1 = (2.8484790054893003, 1.3042633620087096)
U_1 = (3.1351922636826495, 0.720217836059295)
e_1 = Vector(T_1, U_1)
V_1 = (2.859098015052017, -0.7027294453447335)
W_1 = (3.1139542445572164, -1.233679923480565)
f_1 = Vector(V_1, W_1)
Z_1 = (4.356378363395062, 1.813975821019108)
A_2 = (4.643091621588411, 1.1874542568188269)
g_1 = Vector(Z_1, A_2)
B_2 = (5.864277721300823, -1.7009163442400967)
C_2 = (6.150990979494172, -2.295580879752228)
h_1 = Vector(B_2, C_2)
D_2 = (7.8287944904034, -2.2000097936877783)
E_2 = (8.157983786847614, -2.752198290949043)
i_1 = Vector(D_2, E_2)
F_2 = (5.885515740426256, 2.2918312513413563)
G_2 = (6.129752960368739, 1.7290237445173748)
j_1 = Vector(F_2, G_2)
H_2 = Point(p)
I_2 = (8.168602796410331, 2.2281171939650566)
J_2 = (3.9422369904491132, 0.3166954726760631)
L_2 = (4.940423889344476, 1.3148823715714264)
M_2 = (5.067852004097076, 0.7095988264965783)
m_1 = Vector(L_2, M_2)
N_2 = (6.427085228124804, 1.813975821019108)
O_2 = (6.565132352440121, 1.2299302950696933)
n_1 = Vector(N_2, O_2)
P_2 = (7.956222605155999, 2.2918312513413563)
Q_2 = (8.062412700783165, 1.6865477062665084)
p_1 = Vector(P_2, Q_2)
R_2 = (4.92980487978176, -0.6602534070938669)
S_2 = (5.067852004097076, -1.286774971294148)
q_1 = Vector(R_2, S_2)
T_2 = (7.924365576467849, -1.7433923824909632)
U_2 = (8.073031710345882, -2.274342860626795)
r_1 = Vector(T_2, U_2)
V_2 = (1.680387953590471, 1.410453457635876)
W_2 = (2.2750524891026025, 1.5803576106393422)
s_1 = Vector(V_2, W_2)
A_3 = (6.267800084684055, 2.610401538222855)
Z_2 = (5.65189753004649, 2.3130692704667895)
t_1 = Vector(Z_2, A_3)
B_3 = (2.285671498665319, -1.4248220956094644)
C_3 = (2.7847649481130006, -1.552250210362064)
u_2 = Vector(B_3, C_3)
D_3 = (6.278419094246772, -2.4230089945048277)
E_3 = (6.78813155325717, -2.529199090131994)
v_2 = Vector(D_3, E_3)
D = (-3.4596841364194004, 2.159212820981954)
K_2 = (-2.557068323588487, 2.159212820981954)
a = true