2.2.162 Problems 16101 to 16200

Table 2.325: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

16101

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

[[_2nd_order, _missing_x]]

2.227

16102

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

[[_2nd_order, _missing_x]]

1.454

16103

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.095

16104

\[ {}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0 \]
i.c.

[[_Emden, _Fowler]]

1.598

16105

\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0 \]
i.c.

[[_Emden, _Fowler]]

1.613

16106

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.329

16107

\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 0 \]

[[_2nd_order, _missing_x]]

0.855

16108

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

[[_2nd_order, _missing_x]]

2.211

16109

\[ {}y^{\prime \prime }+6 y^{\prime }+18 y = 0 \]

[[_2nd_order, _missing_x]]

2.613

16110

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

[[_2nd_order, _exact, _linear, _homogeneous]]

1.239

16111

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

0.253

16112

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 0 \]

[[_2nd_order, _missing_x]]

0.251

16113

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

[[_2nd_order, _missing_x]]

0.338

16114

\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 0 \]

[[_2nd_order, _missing_x]]

0.241

16115

\[ {}y^{\prime \prime }+9 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

0.498

16116

\[ {}y^{\prime \prime }+49 y = 0 \]

[[_2nd_order, _missing_x]]

0.299

16117

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

[[_Emden, _Fowler]]

0.080

16118

\[ {}t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0 \]

[[_Emden, _Fowler]]

0.083

16119

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

[[_2nd_order, _with_linear_symmetries]]

0.144

16120

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.079

16121

\[ {}a y^{\prime \prime }+b y^{\prime }+c y = 0 \]

[[_2nd_order, _missing_x]]

2.914

16122

\[ {}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0 \]

[[_Emden, _Fowler]]

1.757

16123

\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.083

16124

\[ {}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.158

16125

\[ {}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0 \]

[[_2nd_order, _with_linear_symmetries]]

0.209

16126

\[ {}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0 \]
i.c.

[[_2nd_order, _with_linear_symmetries]]

0.378

16127

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

[[_2nd_order, _quadrature]]

1.953

16128

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

[[_2nd_order, _missing_x]]

0.861

16129

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

[[_2nd_order, _missing_x]]

1.843

16130

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

[[_2nd_order, _missing_x]]

0.892

16131

\[ {}y^{\prime \prime }+8 y^{\prime }+12 y = 0 \]

[[_2nd_order, _missing_x]]

0.886

16132

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

[[_2nd_order, _missing_x]]

1.148

16133

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

0.895

16134

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

[[_2nd_order, _missing_x]]

2.421

16135

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

[[_2nd_order, _missing_x]]

2.303

16136

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

[[_2nd_order, _missing_x]]

2.370

16137

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

[[_2nd_order, _missing_x]]

2.459

16138

\[ {}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0 \]

[[_2nd_order, _missing_x]]

0.908

16139

\[ {}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \]

[[_2nd_order, _missing_x]]

0.895

16140

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

[[_2nd_order, _missing_x]]

1.000

16141

\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

[[_2nd_order, _missing_x]]

1.007

16142

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

[[_2nd_order, _missing_x]]

2.231

16143

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

[[_2nd_order, _missing_x]]

2.599

16144

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

[[_2nd_order, _missing_x]]

1.476

16145

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

[[_2nd_order, _missing_x]]

1.216

16146

\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.476

16147

\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.466

16148

\[ {}y^{\prime \prime }+36 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

19.283

16149

\[ {}y^{\prime \prime }+100 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.253

16150

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

[[_2nd_order, _missing_x]]

1.342

16151

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

[[_2nd_order, _missing_x]]

1.401

16152

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.020

16153

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

3.475

16154

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

[[_2nd_order, _missing_x]]

1.711

16155

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

[[_2nd_order, _missing_x]]

3.204

16156

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

[[_2nd_order, _missing_x]]

3.155

16157

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

[[_2nd_order, _missing_x]]

1.585

16158

\[ {}6 y^{\prime \prime }+5 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

0.885

16159

\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

0.999

16160

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 0 \]

[[_2nd_order, _missing_x]]

2.651

16161

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

[[_Emden, _Fowler]]

1.152

16162

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

[[_Emden, _Fowler]]

1.064

16163

\[ {}a y^{\prime \prime }+2 b y^{\prime }+c y = 0 \]

[[_2nd_order, _missing_x]]

2.912

16164

\[ {}y^{\prime \prime }+6 y^{\prime }+2 y = 0 \]

[[_2nd_order, _missing_x]]

1.244

16165

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]

[[_2nd_order, _missing_x]]

0.888

16166

\[ {}y^{\prime \prime }-6 y^{\prime }-16 y = 0 \]

[[_2nd_order, _missing_x]]

0.900

16167

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

[[_2nd_order, _missing_x]]

2.118

16168

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.514

16169

\[ {}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0 \]

[[_2nd_order, _missing_x]]

0.048

16170

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

[[_2nd_order, _missing_x]]

0.046

16171

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 0 \]
i.c.

[[_2nd_order, _missing_x]]

1.092

16172

\[ {}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t} \]

[[_2nd_order, _with_linear_symmetries]]

2.009

16173

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t} \]

[[_2nd_order, _with_linear_symmetries]]

1.156

16174

\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t} \]

[[_2nd_order, _with_linear_symmetries]]

1.241

16175

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

[[_2nd_order, _with_linear_symmetries]]

1.159

16176

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

[[_2nd_order, _with_linear_symmetries]]

1.223

16177

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

[[_2nd_order, _missing_y]]

2.239

16178

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.829

16179

\[ {}y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

3.342

16180

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.821

16181

\[ {}y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

2.341

16182

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

[[_2nd_order, _quadrature]]

1.896

16183

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

20.851

16184

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

[[_2nd_order, _missing_x]]

1.107

16185

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

[[_2nd_order, _missing_x]]

1.125

16186

\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t \]

[[_2nd_order, _with_linear_symmetries]]

1.171

16187

\[ {}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t \]

[[_2nd_order, _with_linear_symmetries]]

1.247

16188

\[ {}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t \]

[[_2nd_order, _with_linear_symmetries]]

17.122

16189

\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

1.654

16190

\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2} \]

[[_2nd_order, _with_linear_symmetries]]

1.159

16191

\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.328

16192

\[ {}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right ) \]

[[_2nd_order, _missing_y]]

2.835

16193

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

17.544

16194

\[ {}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.880

16195

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.625

16196

\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

2.299

16197

\[ {}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t} \]

[[_2nd_order, _with_linear_symmetries]]

1.158

16198

\[ {}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.335

16199

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t} \]

[[_2nd_order, _linear, _nonhomogeneous]]

1.269

16200

\[ {}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t} \]

[[_2nd_order, _missing_y]]

2.319