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]]

0.129

18102

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

[[_2nd_order, _missing_x]]

1.397

18103

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

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

0.267

18104

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

[[_2nd_order, _missing_x]]

0.735

18105

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

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

1.286

18106

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

[[_2nd_order, _missing_x]]

0.813

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]]

0.750

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]]

0.845

18109

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

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

0.719

18110

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

[[_2nd_order, _missing_x]]

2.035

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]]

0.243

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]]

0.249

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]]

0.397

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]]

0.233

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]]

1.480

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]]

0.306

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]]

0.273

18118

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

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

1.404

18119

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

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

0.709

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]]

0.519

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]]

0.356

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]]

1.014

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]]

1.471

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]]

0.789

18126

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

[[_2nd_order, _missing_x]]

0.141

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]]

0.064

18128

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

[[_2nd_order, _missing_x]]

0.179

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]]

0.237

18130

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

[[_3rd_order, _missing_x]]

0.036

18131

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

[[_2nd_order, _missing_x]]

0.166

18132

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

[[_high_order, _missing_x]]

0.046

18133

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

[[_2nd_order, _missing_x]]

0.177

18134

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

[[_3rd_order, _missing_x]]

0.037

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]]

0.051

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]]

0.288

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]]

0.320

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]]

0.048

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]]

0.052

18140

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

[[_3rd_order, _missing_x]]

0.039

18141

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

[[_3rd_order, _missing_x]]

0.038

18142

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

[[_high_order, _missing_x]]

0.036

18143

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

[[_high_order, _quadrature]]

0.030

18144

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

[[_3rd_order, _missing_x]]

0.033

18145

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

[[_3rd_order, _missing_x]]

0.039

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]]

0.055

18147

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

[[_2nd_order, _missing_x]]

0.567

18148

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

[[_2nd_order, _missing_y]]

0.600

18149

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

[[_2nd_order, _missing_y]]

0.538

18150

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

[[_2nd_order, _missing_y]]

0.570

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]]

0.332

18152

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

[[_2nd_order, _with_linear_symmetries]]

0.296

18153

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

[[_2nd_order, _missing_y]]

0.688

18154

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

[[_2nd_order, _missing_y]]

0.617

18155

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.331

18156

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.343

18157

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.518

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]]

0.344

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]]

0.339

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]]

0.319

18161

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.934

18162

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

[[_2nd_order, _missing_x]]

0.982

18163

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

[[_3rd_order, _with_linear_symmetries]]

0.078

18164

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

[[_3rd_order, _missing_x]]

0.075

18165

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

[[_3rd_order, _missing_x]]

0.068

18166

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

[[_3rd_order, _missing_x]]

0.066

18167

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

[[_high_order, _missing_x]]

0.071

18168

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

[[_high_order, _missing_x]]

0.085

18169

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

[[_high_order, _missing_x]]

0.074

18170

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

[[_high_order, _missing_x]]

0.078

18171

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

[[_high_order, _missing_x]]

0.084

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]]

0.089

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]]

0.094

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]]

0.109

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]]

0.114

18176

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

[[_high_order, _linear, _nonhomogeneous]]

0.105

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]]

0.146

18178

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

[[_high_order, _linear, _nonhomogeneous]]

0.698

18179

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

[[_high_order, _linear, _nonhomogeneous]]

0.128

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]]

0.103

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]]

0.106

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]]

0.116

18183

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

[[_2nd_order, _missing_x]]

0.247

18184

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

[[_2nd_order, _missing_x]]

0.556

18185

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

[[_2nd_order, _missing_x]]

0.833

18186

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

[[_3rd_order, _missing_x]]

0.066

18187

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

[[_3rd_order, _missing_x]]

0.074

18188

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

[[_high_order, _missing_x]]

0.081

18189

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

[[_high_order, _missing_x]]

0.082

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]]

0.102

18191

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

[[_2nd_order, _with_linear_symmetries]]

0.294

18192

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

[[_2nd_order, _missing_y]]

0.610

18193

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

[[_2nd_order, _with_linear_symmetries]]

0.309

18194

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

[[_2nd_order, _with_linear_symmetries]]

0.332

18195

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

[[_2nd_order, _with_linear_symmetries]]

0.262

18196

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

[[_2nd_order, _missing_y]]

0.566

18197

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

[[_2nd_order, _missing_y]]

0.637

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]]

0.304

18199

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

[[_2nd_order, _with_linear_symmetries]]

0.281

18200

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.344