2.2.32 Problems 3101 to 3200

Table 2.81: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

3101

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.063

3102

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.063

3103

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-6 y^{\prime }+2 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.075

3104

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }-4 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.073

3105

\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.057

3106

\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.064

3107

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.067

3108

\begin{align*} 4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.056

3109

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.076

3110

\begin{align*} y^{\prime \prime }-4 y&=3 \cos \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.480

3111

\begin{align*} y^{\prime \prime }+y&=\sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.553

3112

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.486

3113

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.421

3114

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.523

3115

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.454

3116

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.444

3117

\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.118

3118

\begin{align*} y^{\prime \prime }-4 y&=x +{\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.555

3119

\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.815

3120

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=x^{3} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.457

3121

\begin{align*} -2 y^{\prime \prime }+3 y&=x \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.483

3122

\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.652

3123

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=x^{2}+8 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.121

3124

\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{x} \sin \left (3 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.547

3125

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y&=x +{\mathrm e}^{2 x} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.135

3126

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&={\mathrm e}^{4 x} \sin \left (x \right ) \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.138

3127

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=x^{3} {\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.552

3128

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{2 x} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.135

3129

\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\sin \left (k x \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.148

3130

\begin{align*} y^{\prime \prime }+2 n y^{\prime }+n^{2} y&=5 \cos \left (6 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.632

3131

\begin{align*} y^{\prime \prime }+9 y&=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.845

3132

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.781

3133

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=\left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

1.047

3134

\begin{align*} 4 y+y^{\prime \prime }&=8 \sin \left (x \right )^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.659

3135

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.161

3136

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.548

3137

\begin{align*} 4 y+y^{\prime \prime }&=12 \cos \left (x \right )^{2} \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.816

3138

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{-x} \\ y \left (0\right ) &= {\frac {1}{9}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.593

3139

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{x} \sin \left (x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.247

3140

\begin{align*} 2 y^{\prime \prime }+y^{\prime }&=8 \sin \left (2 x \right )+{\mathrm e}^{-x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_y]]

1.532

3141

\begin{align*} y^{\prime \prime }+y&=3 x \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.737

3142

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.681

3143

\begin{align*} 8 y^{\prime \prime }-y&=x \,{\mathrm e}^{-\frac {x}{2}} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.663

3144

\begin{align*} y^{\prime \prime }+y&=\sec \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.602

3145

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.480

3146

\begin{align*} 4 y+y^{\prime \prime }&=x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.447

3147

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.461

3148

\begin{align*} y^{\prime \prime }+y&=4 \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.480

3149

\begin{align*} 4 y+y^{\prime \prime }&=2 x -2 \sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.636

3150

\begin{align*} y^{\prime \prime }-y&=3 x +5 \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.543

3151

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{x}+\sin \left (4 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.646

3152

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }&=\cos \left (2 x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.128

3153

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&={\mathrm e}^{3 x} \\ \end{align*}

[[_3rd_order, _missing_y]]

0.105

3154

\begin{align*} y^{\prime \prime }+y&=\tan \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.577

3155

\begin{align*} y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

2.059

3156

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{2 x} \\ \end{align*}

[[_3rd_order, _missing_y]]

0.109

3157

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}

[[_high_order, _missing_y]]

0.133

3158

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.155

3159

\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.586

3160

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\sin \left ({\mathrm e}^{-x}\right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.591

3161

\begin{align*} 4 y+y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.700

3162

\begin{align*} y^{\prime \prime }-2 y&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.623

3163

\begin{align*} y^{\prime \prime }+9 y&=\sec \left (x \right ) \csc \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.944

3164

\begin{align*} y^{\prime \prime }+9 y&=\csc \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.418

3165

\begin{align*} y^{\prime \prime }+y&=\tan \left (\frac {x}{3}\right )^{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.856

3166

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\tan \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.550

3167

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&={\mathrm e}^{\frac {x}{2}} \ln \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.612

3168

\begin{align*} y^{\prime }+P \left (x \right ) y&=Q \left (x \right ) \\ \end{align*}

[_linear]

2.271

3169

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.471

3170

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.121

3171

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.397

3172

\begin{align*} 4 y+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.415

3173

\begin{align*} y^{\prime \prime }+3 y&=3 \,{\mathrm e}^{-4 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.460

3174

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.621

3175

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{-2 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.385

3176

\begin{align*} y^{\prime \prime }+2 y&=\sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.510

3177

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=\frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.649

3178

\begin{align*} y^{\prime \prime }+3 y^{\prime }-2 y&=\sin \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.471

3179

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{x} \sin \left (x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.404

3180

\begin{align*} y^{\prime \prime \prime }-y&={\mathrm e}^{x} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.106

3181

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y&=\sin \left (x \right )-{\mathrm e}^{4 x} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.655

3182

\begin{align*} -4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.611

3183

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{3 x} \left (1+\sin \left (2 x \right )\right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.741

3184

\begin{align*} y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y&=\sin \left (k x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.629

3185

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.673

3186

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.427

3187

\begin{align*} 4 y+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.442

3188

\begin{align*} y^{\prime \prime }+2 y&=x^{2} {\mathrm e}^{-x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.487

3189

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=x^{2}-8 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.399

3190

\begin{align*} y^{\prime \prime \prime }-y&=x^{2} \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.106

3191

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime }&=x^{2} {\mathrm e}^{-x} \\ \end{align*}

[[_3rd_order, _missing_y]]

0.121

3192

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x^{2} \\ \end{align*}

[[_high_order, _missing_y]]

0.126

3193

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (\sin \left (x \right )-x^{2}\right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.189

3194

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&={\mathrm e}^{2 x} \left (x -3\right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.118

3195

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=\sin \left (3 x \right )+x \,{\mathrm e}^{x} \\ \end{align*}

[[_high_order, _missing_y]]

0.338

3196

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x^{2} {\mathrm e}^{2 x} \\ \end{align*}

[[_3rd_order, _linear, _nonhomogeneous]]

0.135

3197

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime }&=x^{2}+\cos \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.163

3198

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }+2 y&=\sin \left (2 x \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.167

3199

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{3}-\frac {\cos \left (2 x \right )}{2} \\ \end{align*}

[[_high_order, _missing_y]]

0.283

3200

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (x \right ) \\ \end{align*}

[[_3rd_order, _missing_y]]

0.490