2.2.212 Problems 21101 to 21200

Table 2.441: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

21101

\begin{align*} x&=t \left (1+x^{\prime }\right )+x^{\prime } \\ \end{align*}

[_linear]

1.674

21102

\begin{align*} x^{\prime }&=y \\ y^{\prime }&=-x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}

system_of_ODEs

0.322

21103

\begin{align*} x^{\prime }&=a y \\ y^{\prime }&=-a x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}

system_of_ODEs

0.336

21104

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

[[_2nd_order, _missing_x]]

0.841

21105

\begin{align*} x^{\prime \prime }+4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.017

21106

\begin{align*} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

59.761

21107

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{t}+q \left (t \right ) x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

44.109

21108

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

[[_2nd_order, _missing_x]]

0.139

21109

\begin{align*} x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.224

21110

\begin{align*} x^{\prime \prime }+8 x^{\prime }+16 x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.177

21111

\begin{align*} x^{\prime \prime }+2 x^{\prime }-15 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.237

21112

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

[[_2nd_order, _missing_x]]

1.263

21113

\begin{align*} 4 x^{\prime }+2 x^{\prime \prime }&=-5 x \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.325

21114

\begin{align*} x^{\prime \prime }-6 x^{\prime }+9 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.299

21115

\begin{align*} x^{\prime \prime }+x^{\prime }-\beta x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.236

21116

\begin{align*} x^{\prime \prime }+4 x^{\prime }+k x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.242

21117

\begin{align*} x^{\prime \prime }+b x^{\prime }+c x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.369

21118

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

[[_2nd_order, _missing_x]]

0.138

21119

\begin{align*} x^{\prime \prime }+p x^{\prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.779

21120

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

[[_2nd_order, _missing_x]]

0.195

21121

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

[[_2nd_order, _missing_x]]

0.218

21122

\begin{align*} x^{\prime \prime }-2 a x^{\prime }+b x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.349

21123

\begin{align*} x^{\prime \prime }+\lambda ^{2} x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\pi \right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.115

21124

\begin{align*} x^{\prime \prime }+x&=0 \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.575

21125

\begin{align*} x^{\prime \prime }-x&=0 \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.944

21126

\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.221

21127

\begin{align*} x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.207

21128

\begin{align*} x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (\theta \right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.156

21129

\begin{align*} x^{\prime \prime }+2 x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (\infty \right ) &= a \\ \end{align*}

[[_2nd_order, _missing_x]]

18.523

21130

\begin{align*} x^{\prime \prime }-4 x&=t \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.234

21131

\begin{align*} x^{\prime \prime }-4 x&=4 t^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.244

21132

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

[[_2nd_order, _with_linear_symmetries]]

0.238

21133

\begin{align*} x^{\prime \prime }+x&=3 t^{2}+t \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.233

21134

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

[[_2nd_order, _with_linear_symmetries]]

0.242

21135

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

[[_2nd_order, _with_linear_symmetries]]

0.250

21136

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.270

21137

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

[[_2nd_order, _with_linear_symmetries]]

0.296

21138

\begin{align*} x^{\prime \prime }-4 x^{\prime }+13 x&=20 \,{\mathrm e}^{t} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.302

21139

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

[[_2nd_order, _with_linear_symmetries]]

0.259

21140

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.307

21141

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.544

21142

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.267

21143

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.391

21144

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

[[_2nd_order, _missing_y]]

0.573

21145

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

[[_2nd_order, _with_linear_symmetries]]

0.237

21146

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

[[_2nd_order, _with_linear_symmetries]]

0.253

21147

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.270

21148

\begin{align*} x^{\prime \prime }-4 x^{\prime }+3 x&=2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.325

21149

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.384

21150

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.293

21151

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.429

21152

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.622

21153

\begin{align*} x^{\prime \prime }-x&=t \\ x \left (0\right ) &= 0 \\ x \left (1\right ) &= 0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.273

21154

\begin{align*} x^{\prime \prime }+4 x^{\prime }+x&=k \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.349

21155

\begin{align*} x^{\prime \prime }-2 x&=2 \,{\mathrm e}^{t} \\ x \left (0\right ) &= 0 \\ x \left (a \right ) &= 0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.377

21156

\begin{align*} x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5}&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

15.306

21157

\begin{align*} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x&=0 \\ \end{align*}

[[_Emden, _Fowler]]

7.269

21158

\begin{align*} x^{\prime \prime }+2 t^{3} x&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.116

21159

\begin{align*} x^{\prime \prime }-p \left (t \right ) x&=q \left (t \right ) \\ x \left (a \right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

10.412

21160

\begin{align*} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

30.873

21161

\begin{align*} x^{\prime \prime }+x^{\prime }+x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.208

21162

\begin{align*} x^{\prime \prime }-\frac {t x^{\prime }}{4}+x&=0 \\ \end{align*}

[_Lienard]

0.295

21163

\begin{align*} x^{\prime \prime }-\frac {x^{\prime }}{t}&=0 \\ x \left (1\right ) &= 0 \\ x^{\prime }\left (1\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_y]]

0.432

21164

\begin{align*} x^{\prime \prime }-2 x^{\prime } \left (x-1\right )&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

0.745

21165

\begin{align*} x^{\prime \prime }&=2 {x^{\prime }}^{3} x \\ \end{align*}

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

0.205

21166

\begin{align*} x x^{\prime \prime }-2 {x^{\prime }}^{2}-x^{2}&=0 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

6.325

21167

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

0.850

21168

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

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

0.540

21169

\begin{align*} t^{2} x^{\prime \prime }-2 x&=0 \\ \end{align*}

[[_2nd_order, _exact, _linear, _homogeneous]]

0.329

21170

\begin{align*} t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.911

21171

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.875

21172

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

[[_2nd_order, _with_linear_symmetries]]

1.277

21173

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

[[_2nd_order, _with_linear_symmetries]]

0.917

21174

\begin{align*} x^{\prime \prime }-t x^{\prime }+3 x&=0 \\ \end{align*}

[_Hermite]

0.322

21175

\begin{align*} 2 x^{\prime \prime \prime }&=0 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.031

21176

\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.034

21177

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

[[_3rd_order, _missing_x]]

0.041

21178

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

[[_3rd_order, _missing_x]]

0.042

21179

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

[[_3rd_order, _missing_x]]

0.039

21180

\begin{align*} x^{\prime \prime \prime }+4 x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ x^{\prime \prime }\left (0\right ) &= 2 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.087

21181

\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

1.766

21182

\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 1 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.065

21183

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

[[_3rd_order, _missing_x]]

0.062

21184

\begin{align*} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

10.998

21185

\begin{align*} x^{\prime \prime \prime }-3 x^{\prime }+k x&=0 \\ x \left (0\right ) &= 1 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_x]]

8.073

21186

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

[[_high_order, _missing_x]]

0.046

21187

\begin{align*} x^{\prime \prime \prime \prime }-x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ x^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

[[_high_order, _missing_x]]

0.083

21188

\begin{align*} x^{\prime \prime \prime \prime }-x^{\prime \prime }&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

[[_high_order, _missing_x]]

0.059

21189

\begin{align*} x^{\prime \prime \prime \prime }-4 x^{\prime \prime }+x&=0 \\ x \left (0\right ) &= 0 \\ x \left (\infty \right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_high_order, _missing_x]]

0.886

21190

\begin{align*} x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_high_order, _missing_x]]

0.443

21191

\begin{align*} x^{\prime \prime \prime \prime }+2 x^{\prime \prime }-4 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_high_order, _missing_x]]

0.191

21192

\begin{align*} x^{\left (5\right )}-x^{\prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.044

21193

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

[[_high_order, _missing_x]]

0.049

21194

\begin{align*} x^{\left (5\right )}+x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

[[_high_order, _missing_x]]

8.886

21195

\begin{align*} x^{\left (6\right )}-x^{\prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.048

21196

\begin{align*} x^{\left (6\right )}-64 x&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.071

21197

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

[[_high_order, _missing_y]]

0.105

21198

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

[[_3rd_order, _missing_y]]

0.547

21199

\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.075

21200

\begin{align*} x^{\prime \prime \prime }-x^{\prime }&=t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ x^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

[[_3rd_order, _missing_y]]

0.115