Symbolic Solution to Complete Ordinary Differential Equations with Constant Coefficients

Table 2

Numerical error in the symbolic (𝑥_𝑆(𝑡)) and numeric (𝑥_𝑅(𝑡)) approximations, with respect to the exact solution 𝑥(𝑡).

𝑡	|𝑥𝑆(𝑡)−𝑥(𝑡)|	|𝑥𝑅(𝑡)−𝑥(𝑡)|
0.1	0.0000047853239	0.0000001672031
0.4	0.0000712453497	0.0000358751267
0.7	0.0002074165163	0.0003544605868
1.0	0.0003710415717	0.0014307873617
1.3	0.0004547161744	0.0038253117836
1.6	0.0003284030320	0.0080436899562
1.9	0.0000622406880	0.0144197157174
2.2	0.0006216534547	0.0230329551851
2.5	0.0011277539714	0.0336675456541
2.8	0.0013572764337	0.0458134712942
3.1	0.0012347982225	0.0587076431208
3.4	0.0008953272672	0.0714078077594
3.7	0.0006002231245	0.0828896894497
4.0	0.0005492334199	0.0921556872924
4.3	0.0007154938930	0.0983431460014
4.6	0.0008300921248	0.1008204330678
4.9	0.0005487250652	0.0992608551151
5.2	0.0002963137375	0.0936868279861
5.5	0.0015298326576	0.0844798593631
5.8	0.0026838757810	0.0723553936143
6.1	0.0032571351779	0.0583046260627
6.4	0.0030289419613	0.0435091879952
6.7	0.0022189180928	0.0292364988851
7.0	0.0013691340100	0.0167257096706
7.3	0.0010043530807	0.0070750555622
7.6	0.0012821439144	0.0011409176473
7.9	0.0018689726696	0.0005417339524
8.2	0.0021436005756	0.0021897330323
8.5	0.0016148602301	0.0091082291225
8.8	0.0002869277587	0.0196147078451
9.1	0.0012796703448	0.0327897203523
9.4	0.0022771057968	0.0474740017777
9.7	0.0021518593816	0.0623710756305
10.0	0.0009803998394	0.0761625070468