2.2.212 Problems 21101 to 21200

Table 2.437: 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]

3.324

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

0.455

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

0.528

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]]

1.362

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]]

4.804

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]]

1.398

21107

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

[[_2nd_order, _with_linear_symmetries]]

0.945

21108

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

[[_2nd_order, _missing_x]]

0.244

21109

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

[[_2nd_order, _missing_x]]

0.430

21110

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

[[_2nd_order, _missing_x]]

0.312

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]]

0.373

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]]

0.435

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]]

0.681

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]]

0.482

21115

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

[[_2nd_order, _missing_x]]

0.542

21116

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

[[_2nd_order, _missing_x]]

0.570

21117

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

[[_2nd_order, _missing_x]]

0.814

21118

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

[[_2nd_order, _missing_x]]

0.231

21119

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

[[_2nd_order, _missing_x]]

1.922

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]]

0.351

21121

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

[[_2nd_order, _missing_x]]

0.422

21122

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

[[_2nd_order, _missing_x]]

0.788

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]]

3.337

21124

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

[[_2nd_order, _missing_x]]

1.115

21125

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

[[_2nd_order, _missing_x]]

2.962

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]]

0.398

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]]

0.478

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]]

0.412

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]]

1.207

21130

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

[[_2nd_order, _with_linear_symmetries]]

0.368

21131

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

[[_2nd_order, _with_linear_symmetries]]

0.382

21132

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

[[_2nd_order, _with_linear_symmetries]]

0.556

21133

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

[[_2nd_order, _with_linear_symmetries]]

0.548

21134

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

[[_2nd_order, _with_linear_symmetries]]

0.386

21135

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

[[_2nd_order, _with_linear_symmetries]]

0.385

21136

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.423

21137

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

[[_2nd_order, _with_linear_symmetries]]

0.512

21138

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

[[_2nd_order, _with_linear_symmetries]]

0.655

21139

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

[[_2nd_order, _with_linear_symmetries]]

0.420

21140

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.657

21141

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.008

21142

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.618

21143

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.787

21144

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

[[_2nd_order, _missing_y]]

1.126

21145

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

[[_2nd_order, _with_linear_symmetries]]

0.406

21146

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

[[_2nd_order, _with_linear_symmetries]]

0.402

21147

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.434

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]]

0.562

21149

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.763

21150

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.639

21151

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.813

21152

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.101

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]]

0.474

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]]

0.603

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]]

0.664

21156

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

[[_2nd_order, _with_linear_symmetries]]

1.051

21157

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

[[_Emden, _Fowler]]

0.497

21158

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

[[_Emden, _Fowler]]

0.247

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]]

0.698

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]]

0.924

21161

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

[[_2nd_order, _missing_x]]

0.531

21162

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

[_Lienard]

1.147

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]]

0.865

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]]

2.065

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]]

0.495

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]]

9.632

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]]

0.379

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]]

0.232

21169

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

[[_2nd_order, _exact, _linear, _homogeneous]]

0.654

21170

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

[[_Emden, _Fowler]]

2.637

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]]

1.835

21172

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

[[_2nd_order, _with_linear_symmetries]]

2.123

21173

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

[[_2nd_order, _with_linear_symmetries]]

1.619

21174

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

[_Hermite]

1.235

21175

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

[[_3rd_order, _quadrature]]

0.057

21176

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

[[_3rd_order, _missing_x]]

0.060

21177

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

[[_3rd_order, _missing_x]]

0.076

21178

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

[[_3rd_order, _missing_x]]

0.074

21179

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

[[_3rd_order, _missing_x]]

0.065

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]]

0.136

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]]

0.096

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]]

0.094

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]]

0.089

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]]

3.068

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]]

1.856

21186

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

[[_high_order, _missing_x]]

0.077

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]]

0.125

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]]

0.087

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]]

0.173

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]]

0.099

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]]

0.252

21192

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

[[_high_order, _missing_x]]

0.078

21193

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

[[_high_order, _missing_x]]

0.080

21194

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

[[_high_order, _missing_x]]

1.001

21195

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

[[_high_order, _missing_x]]

0.089

21196

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

[[_high_order, _missing_x]]

0.095

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]]

0.150

21198

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

[[_3rd_order, _missing_y]]

0.589

21199

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

[[_3rd_order, _missing_x]]

0.127

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]]

0.172