2.2.132 Problems 13101 to 13200

Table 2.265: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

13101

\[ {}x^{\prime \prime \prime }-x^{\prime }-8 x = 0 \]

[[_3rd_order, _missing_x]]

0.096

13102

\[ {}x^{\prime \prime \prime }+x^{\prime \prime } = 2 \,{\mathrm e}^{t}+3 t^{2} \]

[[_3rd_order, _missing_y]]

0.119

13103

\[ {}x^{\prime \prime \prime }-8 x = 0 \]

[[_3rd_order, _missing_x]]

0.060

13104

\[ {}x^{\prime \prime \prime }+x^{\prime \prime }-x^{\prime }-4 x = 0 \]
i.c.

[[_3rd_order, _missing_x]]

0.371

13105

\[ {}x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_linear, ‘class A‘]]

0.609

13106

\[ {}x^{\prime }+x = \sin \left (2 t \right ) \]
i.c.

[[_linear, ‘class A‘]]

0.520

13107

\[ {}x^{\prime \prime }-x^{\prime }-6 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.318

13108

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.325

13109

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = {\mathrm e}^{-t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.326

13110

\[ {}x^{\prime \prime }-x^{\prime } = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.174

13111

\[ {}x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x = 1-\operatorname {Heaviside}\left (t -5\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

4.338

13112

\[ {}x^{\prime \prime }+9 x = \sin \left (3 t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.384

13113

\[ {}x^{\prime \prime }-2 x = 1 \]
i.c.

[[_2nd_order, _missing_x]]

0.331

13114

\[ {}x^{\prime } = 2 x+\operatorname {Heaviside}\left (t -1\right ) \]
i.c.

[[_linear, ‘class A‘]]

0.561

13115

\[ {}x^{\prime \prime }+4 x = \cos \left (2 t \right ) \operatorname {Heaviside}\left (2 \pi -t \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.842

13116

\[ {}x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right ) \]
i.c.

[[_linear, ‘class A‘]]

0.613

13117

\[ {}x^{\prime } = -x+\operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \]
i.c.

[[_linear, ‘class A‘]]

0.774

13118

\[ {}x^{\prime \prime }+\pi ^{2} x = \pi ^{2} \operatorname {Heaviside}\left (-t +1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.935

13119

\[ {}x^{\prime \prime }-4 x = 1-\operatorname {Heaviside}\left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.882

13120

\[ {}x^{\prime \prime }+3 x^{\prime }+2 x = {\mathrm e}^{-4 t} \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.317

13121

\[ {}x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (-4+t \right ) \]
i.c.

[[_linear, ‘class A‘]]

0.791

13122

\[ {}x^{\prime \prime }-x = \delta \left (t -5\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.532

13123

\[ {}x^{\prime \prime }+x = \delta \left (t -2\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.545

13124

\[ {}x^{\prime \prime }+4 x = \delta \left (t -2\right )-\delta \left (t -5\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.674

13125

\[ {}x^{\prime \prime }+x = 3 \delta \left (t -2 \pi \right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

0.643

13126

\[ {}y^{\prime \prime }+y^{\prime }+y = \delta \left (t -1\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.006

13127

\[ {}x^{\prime \prime }+4 x = \frac {\left (t -5\right ) \operatorname {Heaviside}\left (t -5\right )}{5}+\left (2-\frac {t}{5}\right ) \operatorname {Heaviside}\left (t -10\right ) \]
i.c.

[[_2nd_order, _linear, _nonhomogeneous]]

1.169

13128

\[ {}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=2 x \end {array}\right ] \]

system_of_ODEs

0.533

13129

\[ {}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=-4 x \end {array}\right ] \]

system_of_ODEs

0.524

13130

\[ {}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=2 y \end {array}\right ] \]

system_of_ODEs

0.411

13131

\[ {}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=2 y \end {array}\right ] \]

system_of_ODEs

0.416

13132

\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ] \]

system_of_ODEs

0.439

13133

\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+y \end {array}\right ] \]

system_of_ODEs

0.482

13134

\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=x \end {array}\right ] \]

system_of_ODEs

0.445

13135

\[ {}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-y \end {array}\right ] \]

system_of_ODEs

0.508

13136

\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=-x+4 y \end {array}\right ] \]

system_of_ODEs

0.615

13137

\[ {}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=-2 x+y \end {array}\right ] \]

system_of_ODEs

0.475

13138

\[ {}\left [\begin {array}{c} x^{\prime }=-2 x \\ y^{\prime }=x \end {array}\right ] \]

system_of_ODEs

0.405

13139

\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=-4 y \end {array}\right ] \]

system_of_ODEs

0.444

13140

\[ {}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ] \]

system_of_ODEs

0.450

13141

\[ {}\left [\begin {array}{c} x^{\prime }=-6 y \\ y^{\prime }=6 y \end {array}\right ] \]

system_of_ODEs

0.416

13142

\[ {}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=-x-14 \end {array}\right ] \]

system_of_ODEs

1.237

13143

\[ {}\left [\begin {array}{c} x^{\prime }=3 y-3 x \\ y^{\prime }=x+2 y-1 \end {array}\right ] \]

system_of_ODEs

0.969

13144

\[ {}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-3 y \end {array}\right ] \]

system_of_ODEs

0.449

13145

\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 x-4 y \end {array}\right ] \]

system_of_ODEs

0.448

13146

\[ {}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x-2 y \end {array}\right ] \]

system_of_ODEs

0.591

13147

\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 y-3 x \end {array}\right ] \]

system_of_ODEs

0.707

13148

\[ {}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ] \]
i.c.

system_of_ODEs

0.574

13149

\[ {}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ] \]
i.c.

system_of_ODEs

0.582

13150

\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-3 y \end {array}\right ] \]

system_of_ODEs

0.351

13151

\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ] \]

system_of_ODEs

0.440

13152

\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ] \]

system_of_ODEs

0.454

13153

\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-3 y \end {array}\right ] \]

system_of_ODEs

0.406

13154

\[ {}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y \end {array}\right ] \]

system_of_ODEs

0.470

13155

\[ {}\left [\begin {array}{c} x^{\prime }=-5 x+3 y \\ y^{\prime }=2 x-10 y \end {array}\right ] \]

system_of_ODEs

0.479

13156

\[ {}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=2 y \end {array}\right ] \]

system_of_ODEs

0.305

13157

\[ {}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ] \]

system_of_ODEs

0.542

13158

\[ {}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ] \]

system_of_ODEs

0.433

13159

\[ {}\left [\begin {array}{c} x^{\prime }=9 y \\ y^{\prime }=-x \end {array}\right ] \]

system_of_ODEs

0.498

13160

\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ] \]
i.c.

system_of_ODEs

0.540

13161

\[ {}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ] \]

system_of_ODEs

0.446

13162

\[ {}\left [\begin {array}{c} x^{\prime }=3 x-y+1 \\ y^{\prime }=x+y+2 \end {array}\right ] \]
i.c.

system_of_ODEs

0.667

13163

\[ {}\left [\begin {array}{c} x^{\prime }=-5 x+3 y+{\mathrm e}^{-t} \\ y^{\prime }=2 x-10 y \end {array}\right ] \]

system_of_ODEs

0.509

13164

\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\cos \left (w t \right ) \end {array}\right ] \]

system_of_ODEs

0.778

13165

\[ {}\left [\begin {array}{c} x^{\prime }=3 x+2 y+3 \\ y^{\prime }=7 x+5 y+2 t \end {array}\right ] \]

system_of_ODEs

0.914

13166

\[ {}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ] \]

system_of_ODEs

0.436

13167

\[ {}y^{\prime }+y = x +1 \]

[[_linear, ‘class A‘]]

1.514

13168

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \]

[[_2nd_order, _missing_x]]

0.846

13169

\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \]

[[_2nd_order, _with_linear_symmetries]]

1.148

13170

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0 \]

[[_2nd_order, _exact, _linear, _homogeneous]]

0.870

13171

\[ {}2 x y y^{\prime }+x^{2}+y^{2} = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

58.829

13172

\[ {}x y^{\prime }+y = x^{3} y^{3} \]

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

3.405

13173

\[ {}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x} \]

[[_linear, ‘class A‘]]

1.882

13174

\[ {}y^{\prime }+4 x y = 8 x \]

[_separable]

1.505

13175

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 0 \]

[[_2nd_order, _missing_x]]

0.845

13176

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0 \]

[[_3rd_order, _missing_x]]

0.054

13177

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

[[_3rd_order, _missing_x]]

0.063

13178

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

[[_3rd_order, _fully, _exact, _linear]]

0.116

13179

\[ {}y^{\prime }+2 y = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x} \]

[[_linear, ‘class A‘]]

1.707

13180

\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.437

13181

\[ {}{y^{\prime }}^{2}-4 y = 0 \]

[_quadrature]

0.371

13182

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.430

13183

\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \]
i.c.

[[_linear, ‘class A‘]]

2.069

13184

\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x} \]
i.c.

[[_linear, ‘class A‘]]

2.169

13185

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.417

13186

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.638

13187

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.634

13188

\[ {}y^{\prime \prime }+y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.464

13189

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

0.179

13190

\[ {}y^{\prime } = x^{2} \sin \left (y\right ) \]
i.c.

[_separable]

3.608

13191

\[ {}y^{\prime } = \frac {y^{2}}{-2+x} \]
i.c.

[_separable]

2.594

13192

\[ {}y^{\prime } = y^{{1}/{3}} \]
i.c.

[_quadrature]

2.236

13193

\[ {}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.781

13194

\[ {}y^{2}+3+\left (2 x y-4\right ) y^{\prime } = 0 \]

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

1.563

13195

\[ {}2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0 \]

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

1.307

13196

\[ {}3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0 \]

[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]

1.213

13197

\[ {}6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0 \]

[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

1.757

13198

\[ {}y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0 \]

[_exact, [_Abel, ‘2nd type‘, ‘class A‘]]

12.647

13199

\[ {}\frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime } = 0 \]

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

2.036

13200

\[ {}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0 \]

[_separable]

3.924