2.2.142 Problems 14101 to 14200

Table 2.285: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

14101

\[ {}2 \sqrt {s t}-s+t s^{\prime } = 0 \]

[[_homogeneous, ‘class A‘], _dAlembert]

5.097

14102

\[ {}t -s+t s^{\prime } = 0 \]

[_linear]

1.582

14103

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

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

11.237

14104

\[ {}x \cos \left (\frac {y}{x}\right ) \left (x y^{\prime }+y\right ) = y \sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) \]

[[_homogeneous, ‘class A‘], _dAlembert]

7.654

14105

\[ {}3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

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

3.518

14106

\[ {}x +2 y+1-\left (2 x +4 y+3\right ) y^{\prime } = 0 \]

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

1.918

14107

\[ {}x +2 y+1-\left (2 x -3\right ) y^{\prime } = 0 \]

[_linear]

1.553

14108

\[ {}\frac {y-x y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \]

[[_homogeneous, ‘class A‘], _dAlembert]

14.427

14109

\[ {}\frac {x +y y^{\prime }}{\sqrt {x^{2}+y^{2}}} = m \]

[[_homogeneous, ‘class A‘], _exact, _dAlembert]

39.298

14110

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

12.023

14111

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8.007

14112

\[ {}y^{\prime }-\frac {2 y}{x +1} = \left (x +1\right )^{3} \]

[_linear]

1.763

14113

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

[_linear]

1.670

14114

\[ {}\left (-x^{2}+x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3} = 0 \]

[_linear]

1.516

14115

\[ {}s^{\prime } \cos \left (t \right )+s \sin \left (t \right ) = 1 \]

[_linear]

2.076

14116

\[ {}s^{\prime }+s \cos \left (t \right ) = \frac {\sin \left (2 t \right )}{2} \]

[_linear]

2.479

14117

\[ {}y^{\prime }-\frac {n y}{x} = {\mathrm e}^{x} x^{n} \]

[_linear]

1.433

14118

\[ {}y^{\prime }+\frac {n y}{x} = a \,x^{-n} \]

[_linear]

1.023

14119

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

[[_linear, ‘class A‘]]

1.257

14120

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

[_linear]

1.865

14121

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

[_Bernoulli]

1.481

14122

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

[_separable]

2.568

14123

\[ {}3 y^{2} y^{\prime }-a y^{3}-x -1 = 0 \]

[_rational, _Bernoulli]

1.786

14124

\[ {}y^{\prime } \left (x^{2} y^{3}+x y\right ) = 1 \]

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

1.672

14125

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

[_Bernoulli]

2.553

14126

\[ {}y-\cos \left (x \right ) y^{\prime } = y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \]

[_Bernoulli]

6.335

14127

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

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

1.319

14128

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

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

1.342

14129

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

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

2.457

14130

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

[_exact, _rational]

2.029

14131

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

[_exact, _rational]

1.517

14132

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

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

2.665

14133

\[ {}\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}} = \frac {2 y y^{\prime }}{x^{3}} \]

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

7.054

14134

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

[_separable]

2.949

14135

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

[[_1st_order, _with_linear_symmetries], _exact, _rational]

1.868

14136

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.424

14137

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

[[_homogeneous, ‘class C‘], _rational, _dAlembert]

0.503

14138

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.494

14139

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.719

14140

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

[_quadrature]

0.418

14141

\[ {}y = x y^{\prime }+\sqrt {1-{y^{\prime }}^{2}} \]

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

1.912

14142

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

[_separable]

1.730

14143

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

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

0.441

14144

\[ {}y = x y^{\prime }-\frac {1}{{y^{\prime }}^{2}} \]

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.680

14145

\[ {}y^{\prime } = \frac {2 y}{x}-\sqrt {3} \]

[_linear]

2.723

14146

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

[[_3rd_order, _missing_x]]

0.053

14147

\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]

1.191

14148

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

[[_3rd_order, _quadrature]]

0.165

14149

\[ {}y^{\prime \prime } = a^{2} y \]

[[_2nd_order, _missing_x]]

1.648

14150

\[ {}y^{\prime \prime } = \frac {a}{y^{3}} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2.239

14151

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

[[_2nd_order, _missing_y]]

1.283

14152

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

0.283

14153

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

[[_2nd_order, _missing_y]]

1.513

14154

\[ {}{y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2} \]
i.c.

[[_2nd_order, _missing_x]]

4.860

14155

\[ {}y^{\prime \prime } = \frac {1}{2 y^{\prime }} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]

1.263

14156

\[ {}y^{\prime \prime \prime } = {y^{\prime \prime }}^{2} \]

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

0.368

14157

\[ {}y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2} = 0 \]

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

0.616

14158

\[ {}y^{\prime \prime } = 9 y \]

[[_2nd_order, _missing_x]]

2.006

14159

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

[[_2nd_order, _missing_x]]

2.049

14160

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

[[_2nd_order, _missing_x]]

2.027

14161

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

[[_2nd_order, _missing_x]]

0.847

14162

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

[[_2nd_order, _missing_x]]

0.972

14163

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]

[[_2nd_order, _missing_x]]

2.549

14164

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

[[_2nd_order, _missing_x]]

1.115

14165

\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

0.988

14166

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

[[_2nd_order, _missing_x]]

2.103

14167

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \]

[[_high_order, _missing_x]]

0.064

14168

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

[[_3rd_order, _missing_x]]

0.053

14169

\[ {}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y = 0 \]

[[_3rd_order, _missing_x]]

0.058

14170

\[ {}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 0 \]

[[_high_order, _missing_x]]

0.062

14171

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0 \]

[[_high_order, _missing_x]]

0.075

14172

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \]

[[_high_order, _missing_x]]

0.056

14173

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

[[_high_order, _missing_x]]

0.066

14174

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

[[_high_order, _missing_x]]

0.066

14175

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

[[_2nd_order, _with_linear_symmetries]]

1.142

14176

\[ {}s^{\prime \prime }-a^{2} s = t +1 \]

[[_2nd_order, _with_linear_symmetries]]

0.824

14177

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.481

14178

\[ {}y^{\prime \prime }-y = 5 x +2 \]

[[_2nd_order, _with_linear_symmetries]]

1.117

14179

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

[[_2nd_order, _with_linear_symmetries]]

0.684

14180

\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \]

[[_2nd_order, _with_linear_symmetries]]

1.125

14181

\[ {}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

[[_2nd_order, _with_linear_symmetries]]

2.793

14182

\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \]

[[_2nd_order, _missing_y]]

2.101

14183

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

[[_2nd_order, _linear, _nonhomogeneous]]

76.711

14184

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.655

14185

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3 \]

[[_3rd_order, _with_linear_symmetries]]

0.099

14186

\[ {}y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \]

[[_high_order, _linear, _nonhomogeneous]]

0.153

14187

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

[[_high_order, _linear, _nonhomogeneous]]

0.838

14188

\[ {}y^{\prime \prime }+2 h y^{\prime }+n^{2} y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

4.642

14189

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.461

14190

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.414

14191

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.928

14192

\[ {}y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.192

14193

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

system_of_ODEs

0.637

14194

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

system_of_ODEs

0.560

14195

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

system_of_ODEs

0.709

14196

\[ {}y^{\prime \prime } y = 1+{y^{\prime }}^{2} \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.288

14197

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

[_separable]

2.912

14198

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

[[_homogeneous, ‘class C‘], _rational, _dAlembert]

0.515

14199

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.855

14200

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

[_linear]

1.944