实验十一级数与方程符号求解docWord格式文档下载.docx
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(1/2)V(1/3)+2/(972+12*6465"
(1/2)V(1/3)-l/2*i*3"
(1/2)厂(1/3)+4/(972+12
*646571/2))71/3))厂2
-1
(3)>
x=solve(’3*x*exp(x)+5*sin(x)-78.5’,’x’)
1.1438132465904248768705131138349-3.51405764594581256962917
45801210*i
(4)>
[xy]=solve(’sqrt(x*x+y*y)-100’,’3*x+5*y-8’,’x,y’)
12/17-10/17*2124671/2)
12/17+10/17*21246^(1/2)
20/17+6/17*21246"
(1/2)20/17-6/17*2124671/2)
4、求微分方程初值问题的符号解,并与数值解进行比较。
^2+4^+29^0
dx一dx
^(0)=0^'
(0)=15
functiondy=vdp29(t,y)
dy=zeros(2,1);
dy⑴二y⑵;
dy
(2)=-4*y
(2)-29*y(l);
[ty]=ode45(’vdp29’,[010],[0,15])
0.0000
0.0001
0.0002
0.0003
0.0004
0.0008
0.0013
0.0017
0.0021
0.0042
0.0063
0.0084
0.0105
0.0209
0.0314
0.0419
0.0523
0.0892
0.1260
0.1628
0.1996
0.2377
0.2757
0.3138
0.3518
0.4269
0.4644
0.5019
0.5397
0.5775
0.6153
0.6531
0.6908
0.7284
0.7660
0.8037
0.8416
0.8795
0.9174
0.9553
0.9928
1.0303
1.0678
1.1052
1.1430
1.1807
1.2939
1.3315
1.3691
1.4067
1.4445
1.4824
1.5203
1.5581
1.5961
1.6341
1.6721
1.7101
L7478
1.7855
1.8232
1.8609
1.8985
1.9360
1.9736
2.0112
2.0868
2.1246
2.1625
2.2007
2.2389
2.2772
2.3154
2.3531
2.3907
2.4284
2.4661
2.5036
2.5411
2.5786
2.6161
2.6539
2.6917
2.7295
2.7672
2.8054
2.8435
2.9198
2.9574
2.9950
3.0326
3.0703
3.1077
3.1452
3.1826
3.2201
3.2578
3.2955
3.3333
3.3710
3.4091
3.4471
3.4852
3.5232
3.5608
3.5984
3.6360
3.6735
3.7492
3.7871
3.8249
3.8626
3.9003
3.9380
3.9757
4.0137
4.0517
4.0896
4.1276
4.1659
4.2043
4.2426
4.2809
4.3201
4.3594
4.3986
4.4378
4.4754
4.5131
4.5883
4.6263
4.6642
4.7022
4.7401
4.7870
4.8339
4.8808
4.9276
4.9694
5.0111
5.0529
5.0946
5.1336
5.1725
5.2114
5.2503
5.2947
5.3390
5.3834
5.4277
5.5542
5.6174
5.6806
5.7319
5.7832
5.8344
5.8857
5.9390
5.9923
6.0456
6.0989
6.1636
6.2283
6.2930
6.3577
6.4224
6.4871
6.5519
6.6166
6.6869
6.7572
6.8979
6.9949
7.0919
7.1889
7.2859
7.3678
7.4498
7.5317
7.6136
7.7317
7.8499
7.9680
8.0861
8.1968
8.3075
8.4183
8.5290
8.6726
8.8163
8.9599
9.1036
9.4971
9.6939
9.8907
9.9180
9.9453
9.9727
10.0000
y=
15.0000
14.9998
14.9996
14.9994
14.9992
0.0005
14.9982
0.0007
14.9972
0.0010
14.9962
0.0012
14.9952
0.0025
14.9902
0.0037
14.9851
0.0050
14.9801
0.0062
14.9751
0.012514.9499
0.0187
14.9247
0.0250
14.8995
0.0312
14.8742
0.0622
14.7473
0.0930
14.6197
0.1234
14.4912
0.1536
14.3620
0.3005
13.7054
0.4405
13.0330
0.5733
12.3476
0.6989
11.6520
1.0822
9.1573
1.3736
6.6709
1.5749
4.2848
1.6912
2.0697
1.7299
0.0192
1.6960
-1.7426
1.6014
-3.1866
1.4581
-4.3028
1.2807
-5.0868
1.0796
-5.5694
6497
-5.7327
4371
-5.4768
2376
-5.0471
0572
-4.4854
1000
-3.8308
2310
-3.1229
3350
-2.3954
4116
-1.6795
4618
-0.9999
4876
-0.3723
4909
0.1813
4749
0.6495
4429
1.0267
3988
1.3087
3458
1.5022
2872
1.6122
2260
1.6461
1643
1.6126
1049
1.5221
0499
1.3864
0007
1.2168
0415
1.0249
0762
0.8209
1032
0.6146
1225
0.4138
1345
0.2238
1397
0.0519
1387
-0.0976
1326
-0.2223
1222
-0.3214
1085
-0.3940
0926
-0.4412
0753
-0.4646
0577
-0.4668
0403
-0.4508
0239
-0.4200
0088
-0.3775
0044
-0.3267
0157
-0.2706
0247
-0.2121
0316
-0.1538
0363
-0.0974
0390
一0.0451
03980.0015
0.0415
0367
0.0746
0334
0.1001
0292
0.1181
0244
0.1289
0195
0.1331
0145
0.1316
0096
0.1254
0051
0.1152
0010
0.1021
0025
0.0870
0055
0.0708
0078
0.0541
0.0376
0107
0.0219
0112
0.0077
0113
-0.0049
0109
-0.0156
0101
-0.0242
0091
-0.0306
一0.0350
0065-o.0373
0050
-0.0379
0036
-0.0369
0023
-0.0347
-0.0315
0001
-0.0276
-0.0232
0018
-0.0185
0024
-0.0137
0029
-0.0091
0031
-0.0048
0032
-0.0009
0030
0.0054
0028
0.0076
0.0092
0021
0.0102
0017
0.0107
0013
0009
0.0103
0005
0.0096
0002
0.0086
0.0074
0004
0.0061
0006
0.0047
0.0034
0008
0.0021
0.0009
-0.0001
-0.0010
-0.0018
-0.0023
-0.0027
-0.0030
-0.0031
0003
-0.0030
-0.0029
-0.0026
0000
-0.0023
-0.0019
-0.0015
-0.0011
-0.0008
一0.0004
0.0006
0.0001
-0.0001
-0.0002
-0.0002
一0.0002
-0.0000
-0.0000
一0.0000
»
plot(t,y(:
,1),’一’)
0.0000-0.0000
5、求微分方程组的通解。
dx
dt
=2x-3y+3z
dy
=4x-5y+3z
dzAA—=4x-4y+2zdt
[x,y,z]=dsolve(’Dx=2*x_3*y+3*z’,’Dy=4*x_5*y+3*z’,’Dz=4*x-4*y+2*z’,’f)
C2^exp(-t)+C3^exp(2*t)
C2*cxp(~t)+C3*cxp(2*t)+cxp(-2*t)*C1
C3*exp(2*t)+exp(-2*t)*C1