2.2.182 Problems 18101 to 18200

Table 2.381: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

18101

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

[[_3rd_order, _missing_y]]

0.407

18102

\begin{align*} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\ \end{align*}

[[_2nd_order, _missing_x]]

7.763

18103

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

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

1.209

18104

\begin{align*} y^{\prime \prime }&=\sqrt {1-{y^{\prime }}^{2}} \\ \end{align*}

[[_2nd_order, _missing_x]]

4.682

18105

\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}

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

6.194

18106

\begin{align*} y^{\prime \prime }&=\sqrt {y^{\prime }+1} \\ \end{align*}

[[_2nd_order, _missing_x]]

3.538

18107

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

[[_2nd_order, _missing_x]]

1.582

18108

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

[[_2nd_order, _missing_x]]

4.220

18109

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

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

4.583

18110

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

[[_2nd_order, _missing_x]]

11.332

18111

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

[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

1.671

18112

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

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

1.750

18113

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

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

0.560

18114

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

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

0.405

18115

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

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

1.684

18116

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

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

1.196

18117

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

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

1.611

18118

\begin{align*} y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}

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

9.389

18119

\begin{align*} 2 y y^{\prime \prime }&=1+{y^{\prime }}^{2} \\ \end{align*}

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

6.252

18120

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

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

0.954

18121

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

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

1.687

18122

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

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

0.826

18123

\begin{align*} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2}&=4 y^{2} \\ \end{align*}

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

5.405

18124

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

[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]

0.065

18125

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

[[_2nd_order, _missing_x]]

3.020

18126

\begin{align*} 3 y^{\prime \prime }-2 y^{\prime }-8 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.366

18127

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

[[_3rd_order, _missing_x]]

0.157

18128

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

[[_2nd_order, _missing_x]]

0.491

18129

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.503

18130

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.102

18131

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

[[_2nd_order, _missing_x]]

0.395

18132

\begin{align*} y^{\left (6\right )}+2 y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.128

18133

\begin{align*} 4 y^{\prime \prime }-8 y^{\prime }+5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.412

18134

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

[[_3rd_order, _missing_x]]

0.068

18135

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+10 y^{\prime \prime }+12 y^{\prime }+5 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.119

18136

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

[[_2nd_order, _missing_x]]

1.099

18137

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

[[_2nd_order, _missing_x]]

0.635

18138

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-5 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.113

18139

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }-6 y^{\prime }-4 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.122

18140

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

[[_3rd_order, _missing_x]]

0.100

18141

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

[[_3rd_order, _missing_x]]

0.099

18142

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

[[_high_order, _missing_x]]

0.070

18143

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

[[_high_order, _quadrature]]

0.071

18144

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

[[_3rd_order, _missing_x]]

0.099

18145

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

[[_3rd_order, _missing_x]]

0.097

18146

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

[[_3rd_order, _missing_x]]

0.094

18147

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

[[_2nd_order, _missing_x]]

1.993

18148

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.436

18149

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

[[_2nd_order, _missing_y]]

1.352

18150

\begin{align*} y^{\prime \prime }+7 y^{\prime }&={\mathrm e}^{-7 x} \\ \end{align*}

[[_2nd_order, _missing_y]]

1.379

18151

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=\left (1-x \right ) {\mathrm e}^{4 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.773

18152

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&={\mathrm e}^{5 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.717

18153

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

[[_2nd_order, _missing_y]]

1.599

18154

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

[[_2nd_order, _missing_y]]

1.479

18155

\begin{align*} y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.292

18156

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.768

18157

\begin{align*} y^{\prime \prime }+16 y&=\sin \left (4 x +\alpha \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.167

18158

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.710

18159

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.713

18160

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 x} \cos \left (2 x \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.682

18161

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.715

18162

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

[[_2nd_order, _missing_x]]

5.959

18163

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

[[_3rd_order, _with_linear_symmetries]]

0.168

18164

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y&=1 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.203

18165

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

[[_3rd_order, _missing_x]]

0.162

18166

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

[[_3rd_order, _missing_x]]

0.161

18167

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

[[_high_order, _missing_x]]

0.173

18168

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

[[_high_order, _missing_x]]

0.223

18169

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

[[_high_order, _missing_x]]

0.221

18170

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

[[_high_order, _missing_x]]

0.218

18171

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }&=1 \\ \end{align*}

[[_high_order, _missing_x]]

0.225

18172

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

[[_high_order, _missing_y]]

0.223

18173

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

[[_high_order, _missing_y]]

0.233

18174

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

[[_high_order, _missing_y]]

0.245

18175

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

[[_high_order, _linear, _nonhomogeneous]]

0.259

18176

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

[[_high_order, _linear, _nonhomogeneous]]

0.241

18177

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

[[_high_order, _linear, _nonhomogeneous]]

0.421

18178

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

[[_high_order, _linear, _nonhomogeneous]]

1.326

18179

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

[[_high_order, _linear, _nonhomogeneous]]

0.275

18180

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.239

18181

\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{x} \\ \end{align*}

[[_high_order, _with_linear_symmetries]]

0.256

18182

\begin{align*} y-4 y^{\prime }+6 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}

[[_high_order, _linear, _nonhomogeneous]]

0.263

18183

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

[[_2nd_order, _missing_x]]

0.599

18184

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

[[_2nd_order, _missing_x]]

2.002

18185

\begin{align*} y^{\prime \prime }+9 y&=9 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.359

18186

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=1 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.155

18187

\begin{align*} 5 y^{\prime \prime \prime }-7 y^{\prime \prime }&=3 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.204

18188

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

[[_high_order, _missing_x]]

0.227

18189

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

[[_high_order, _missing_x]]

0.219

18190

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \\ \end{align*}

[[_high_order, _missing_x]]

0.190

18191

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

[[_2nd_order, _with_linear_symmetries]]

0.732

18192

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

[[_2nd_order, _missing_y]]

1.457

18193

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

[[_2nd_order, _with_linear_symmetries]]

0.759

18194

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

[[_2nd_order, _with_linear_symmetries]]

0.737

18195

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.604

18196

\begin{align*} 7 y^{\prime \prime }-y^{\prime }&=14 x \\ \end{align*}

[[_2nd_order, _missing_y]]

1.385

18197

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

[[_2nd_order, _missing_y]]

1.469

18198

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=10 \left (1-x \right ) {\mathrm e}^{-2 x} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.635

18199

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=x +1 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.171

18200

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.776