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]

4.004

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

0.543

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

0.576

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]]

2.837

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]]

5.717

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]]

8.315

21107

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

[[_2nd_order, _with_linear_symmetries]]

8.681

21108

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

[[_2nd_order, _missing_x]]

7.092

21109

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

[[_2nd_order, _missing_x]]

4.420

21110

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

[[_2nd_order, _missing_x]]

6.928

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]]

1.147

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]]

14.719

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]]

12.470

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]]

9.249

21115

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

[[_2nd_order, _missing_x]]

16.281

21116

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

[[_2nd_order, _missing_x]]

15.339

21117

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

[[_2nd_order, _missing_x]]

17.819

21118

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

[[_2nd_order, _missing_x]]

4.117

21119

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

[[_2nd_order, _missing_x]]

5.160

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]]

1.747

21121

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

[[_2nd_order, _missing_x]]

6.623

21122

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

[[_2nd_order, _missing_x]]

17.945

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]]

5.820

21124

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

[[_2nd_order, _missing_x]]

2.197

21125

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

[[_2nd_order, _missing_x]]

3.915

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]]

1.139

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]]

1.588

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]]

1.128

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]]

7.836

21130

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

[[_2nd_order, _with_linear_symmetries]]

10.611

21131

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

[[_2nd_order, _with_linear_symmetries]]

10.348

21132

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

[[_2nd_order, _with_linear_symmetries]]

10.282

21133

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

[[_2nd_order, _with_linear_symmetries]]

8.641

21134

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

[[_2nd_order, _with_linear_symmetries]]

23.117

21135

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

[[_2nd_order, _with_linear_symmetries]]

22.762

21136

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

[[_2nd_order, _linear, _nonhomogeneous]]

22.845

21137

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

[[_2nd_order, _with_linear_symmetries]]

24.343

21138

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

[[_2nd_order, _with_linear_symmetries]]

22.755

21139

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

[[_2nd_order, _with_linear_symmetries]]

36.213

21140

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.791

21141

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.158

21142

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

[[_2nd_order, _linear, _nonhomogeneous]]

21.249

21143

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

[[_2nd_order, _linear, _nonhomogeneous]]

3.239

21144

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

[[_2nd_order, _missing_y]]

4.975

21145

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

[[_2nd_order, _with_linear_symmetries]]

23.392

21146

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

[[_2nd_order, _with_linear_symmetries]]

22.600

21147

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

[[_2nd_order, _linear, _nonhomogeneous]]

36.130

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]]

35.958

21149

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

[[_2nd_order, _linear, _nonhomogeneous]]

22.873

21150

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

[[_2nd_order, _linear, _nonhomogeneous]]

22.880

21151

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

[[_2nd_order, _linear, _nonhomogeneous]]

21.538

21152

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

[[_2nd_order, _linear, _nonhomogeneous]]

23.012

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]]

14.548

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]]

3.763

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]]

31.135

21156

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

[[_2nd_order, _with_linear_symmetries]]

5.107

21157

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

[[_Emden, _Fowler]]

2.864

21158

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

[[_Emden, _Fowler]]

1.952

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]]

2.189

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]]

5.829

21161

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

[[_2nd_order, _missing_x]]

17.645

21162

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

[_Lienard]

5.521

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]]

20.930

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]]

3.571

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]]

1.069

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]]

13.199

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]]

0.423

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]]

0.287

21169

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

[[_2nd_order, _exact, _linear, _homogeneous]]

2.833

21170

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

[[_Emden, _Fowler]]

10.869

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]]

4.362

21172

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

[[_2nd_order, _with_linear_symmetries]]

4.579

21173

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

[[_2nd_order, _with_linear_symmetries]]

4.702

21174

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

[_Hermite]

5.365

21175

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

[[_3rd_order, _quadrature]]

0.077

21176

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

[[_3rd_order, _missing_x]]

0.074

21177

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

[[_3rd_order, _missing_x]]

0.084

21178

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

[[_3rd_order, _missing_x]]

0.087

21179

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

[[_3rd_order, _missing_x]]

0.082

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]]

0.166

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]]

0.147

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]]

0.108

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]]

0.087

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]]

2.569

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]]

1.925

21186

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

[[_high_order, _missing_x]]

0.053

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]]

0.115

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]]

0.049

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]]

0.138

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]]

0.065

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]]

0.223

21192

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

[[_high_order, _missing_x]]

0.049

21193

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

[[_high_order, _missing_x]]

0.053

21194

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

[[_high_order, _missing_x]]

0.307

21195

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

[[_high_order, _missing_x]]

0.051

21196

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

[[_high_order, _missing_x]]

0.077

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]]

0.094

21198

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

[[_3rd_order, _missing_y]]

0.560

21199

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

[[_3rd_order, _missing_x]]

0.081

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]]

0.118