2.2.122 Problems 12101 to 12200

Table 2.245: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

12101

\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+\lambda \sin \left (\lambda x \right )^{3} \]

[_Riccati]

9.033

12102

\[ {}2 y^{\prime } = \left (\lambda +a -a \sin \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \sin \left (\lambda x \right ) \]

[_Riccati]

75.392

12103

\[ {}y^{\prime } = \left (\lambda +a \sin \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \sin \left (\lambda x \right )^{2} \]

[_Riccati]

34.690

12104

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \sin \left (x \right )^{m} y-a \sin \left (x \right )^{m} \]

[_Riccati]

29.863

12105

\[ {}y^{\prime } = a \sin \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

67.362

12106

\[ {}y^{\prime } x = a \sin \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \sin \left (\lambda x \right )^{m} \]

[_Riccati]

20.188

12107

\[ {}\left (a \sin \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \sin \left (\mu x \right ) y-d^{2}+c d \sin \left (\mu x \right ) \]

[_Riccati]

116.788

12108

\[ {}\left (a \sin \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \sin \left (\lambda x \right ) = 0 \]

[_Riccati]

6.140

12109

\[ {}y^{\prime } = \alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right ) \]

[_Riccati]

3.433

12110

\[ {}y^{\prime } = y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \cos \left (\lambda x \right )^{2} \]

[_Riccati]

7.047

12111

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+c \cos \left (\lambda x +a \right )^{n} \cos \left (\lambda x +b \right )^{-n -4} \]

[_Riccati]

171.799

12112

\[ {}y^{\prime } = y^{2}+a \cos \left (\beta x \right ) y+a b \cos \left (\beta x \right )-b^{2} \]

[_Riccati]

4.863

12113

\[ {}y^{\prime } = y^{2}+a \cos \left (b x \right )^{m} y+a \cos \left (b x \right )^{m} \]

[_Riccati]

15.582

12114

\[ {}y^{\prime } = \lambda \cos \left (\lambda x \right ) y^{2}+\lambda \cos \left (\lambda x \right )^{3} \]

[_Riccati]

9.213

12115

\[ {}2 y^{\prime } = \left (\lambda +a -a \cos \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \cos \left (\lambda x \right ) \]

[_Riccati]

45.522

12116

\[ {}y^{\prime } = \left (\lambda +a \cos \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \cos \left (\lambda x \right )^{2} \]

[_Riccati]

30.873

12117

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \cos \left (x \right )^{m} y-a \cos \left (x \right )^{m} \]

[_Riccati]

26.480

12118

\[ {}y^{\prime } = a \cos \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

38.077

12119

\[ {}y^{\prime } x = a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m} \]

[_Riccati]

49.958

12120

\[ {}\left (a \cos \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right ) \]

[_Riccati]

120.366

12121

\[ {}\left (a \cos \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \cos \left (\lambda x \right ) = 0 \]

[_Riccati]

5.884

12122

\[ {}y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \]

[_Riccati]

12.207

12123

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2} \]

[_Riccati]

16.151

12124

\[ {}y^{\prime } = a y^{2}+b \tan \left (x \right ) y+c \]

[_Riccati]

5.708

12125

\[ {}y^{\prime } = a y^{2}+2 a b \tan \left (x \right ) y+b \left (a b -1\right ) \tan \left (x \right )^{2} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

9.747

12126

\[ {}y^{\prime } = y^{2}+a \tan \left (\beta x \right ) y+a b \tan \left (\beta x \right )-b^{2} \]

[_Riccati]

20.800

12127

\[ {}y^{\prime } = y^{2}+a x \tan \left (b x \right )^{m} y+a \tan \left (b x \right )^{m} \]

[_Riccati]

12.073

12128

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \tan \left (x \right )^{m} y-a \tan \left (x \right )^{m} \]

[_Riccati]

24.304

12129

\[ {}y^{\prime } = a \tan \left (\lambda x \right )^{n} y^{2}-a \,b^{2} \tan \left (\lambda x \right )^{n +2}+b \lambda \tan \left (\lambda x \right )^{2}+b \lambda \]

[_Riccati]

39.214

12130

\[ {}y^{\prime } = a \tan \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

148.680

12131

\[ {}y^{\prime } x = a \tan \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \tan \left (\lambda x \right )^{m} \]

[_Riccati]

68.287

12132

\[ {}\left (a \tan \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right ) \]

[_Riccati]

78.172

12133

\[ {}y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \]

[_Riccati]

12.200

12134

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2} \]

[_Riccati]

16.786

12135

\[ {}y^{\prime } = y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2} \]

[_Riccati]

82.316

12136

\[ {}y^{\prime } = y^{2}+a \cot \left (\beta x \right ) y+a b \cot \left (\beta x \right )-b^{2} \]

[_Riccati]

6.357

12137

\[ {}y^{\prime } = y^{2}+a x \cot \left (b x \right )^{m} y+a \cot \left (b x \right )^{m} \]

[_Riccati]

10.001

12138

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \cot \left (x \right )^{m} y-a \cot \left (x \right )^{m} \]

[_Riccati]

24.309

12139

\[ {}y^{\prime } = a \cot \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

194.002

12140

\[ {}y^{\prime } x = a \cot \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cot \left (\lambda x \right )^{m} \]

[_Riccati]

68.172

12141

\[ {}\left (a \cot \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cot \left (\mu x \right ) y-d^{2}+c d \cot \left (\mu x \right ) \]

[_Riccati]

94.583

12142

\[ {}y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x \right )^{n} \cos \left (\lambda x \right )^{-n -4} \]

[_Riccati]

31.242

12143

\[ {}y^{\prime } = a \sin \left (\lambda x \right ) y^{2}+b \sin \left (\lambda x \right ) \cos \left (\lambda x \right )^{n} \]

[_Riccati]

12.788

12144

\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \cos \left (\lambda x \right )^{n} y-a \cos \left (\lambda x \right )^{n -1} \]

[_Riccati]

51.904

12145

\[ {}y^{\prime } = a \cos \left (\lambda x \right ) y^{2}+b \cos \left (\lambda x \right ) \sin \left (\lambda x \right )^{n} \]

[_Riccati]

35.021

12146

\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \,x^{n} \cos \left (\lambda x \right ) y-a \,x^{n} \]

[_Riccati]

16.336

12147

\[ {}\sin \left (2 x \right )^{n +1} y^{\prime } = a y^{2} \sin \left (x \right )^{2 n}+b \cos \left (x \right )^{2 n} \]

[_Riccati]

71.024

12148

\[ {}y^{\prime } = y^{2}-y \tan \left (x \right )+a \left (1-a \right ) \cot \left (x \right )^{2} \]

[_Riccati]

7.889

12149

\[ {}y^{\prime } = y^{2}-m y \tan \left (x \right )+b^{2} \cos \left (x \right )^{2 m} \]

[_Riccati]

37.759

12150

\[ {}y^{\prime } = y^{2}+m y \cot \left (x \right )+b^{2} \sin \left (x \right )^{2 m} \]

[_Riccati]

39.573

12151

\[ {}y^{\prime } = y^{2}-2 \lambda ^{2} \tan \left (x \right )^{2}-2 \lambda ^{2} \cot \left (\lambda x \right )^{2} \]

[_Riccati]

23.613

12152

\[ {}y^{\prime } = y^{2}+a \lambda +b \lambda +2 a b +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}+b \left (\lambda -b \right ) \cot \left (\lambda x \right )^{2} \]

[_Riccati]

19.474

12153

\[ {}y^{\prime } = y^{2}-\frac {\lambda ^{2}}{2}-\frac {3 \lambda ^{2} \tan \left (\lambda x \right )^{2}}{4}+a \cos \left (\lambda x \right )^{2} \sin \left (\lambda x \right )^{n} \]

[_Riccati]

38.376

12154

\[ {}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \sin \left (\lambda x \right ) y-a \tan \left (\lambda x \right ) \]

[_Riccati]

14.741

12155

\[ {}y^{\prime } = y^{2}+\lambda \arcsin \left (x \right )^{n} y-a^{2}+a \lambda \arcsin \left (x \right )^{n} \]

[_Riccati]

3.920

12156

\[ {}y^{\prime } = y^{2}+\lambda x \arcsin \left (x \right )^{n} y+\lambda \arcsin \left (x \right )^{n} \]

[_Riccati]

11.490

12157

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arcsin \left (x \right )^{n} \left (x^{k +1} y-1\right ) \]

[_Riccati]

51.264

12158

\[ {}y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arcsin \left (x \right )^{n} \]

[_Riccati]

10.191

12159

\[ {}y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arcsin \left (x \right )^{n} y+b m \,x^{m -1} \]

[_Riccati]

28.523

12160

\[ {}y^{\prime } = \lambda \arcsin \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arcsin \left (x \right )^{n} \]

[_Riccati]

49.904

12161

\[ {}y^{\prime } = \lambda \arcsin \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

346.630

12162

\[ {}y^{\prime } x = \lambda \arcsin \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arcsin \left (x \right )^{n} \]

[_Riccati]

152.265

12163

\[ {}y^{\prime } x = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arcsin \left (x \right )^{m}-n y \]

[_Riccati]

143.791

12164

\[ {}y^{\prime } = y^{2}+\lambda \arccos \left (x \right )^{n} y-a^{2}+a \lambda \arccos \left (x \right )^{n} \]

[_Riccati]

7.165

12165

\[ {}y^{\prime } = y^{2}+\lambda x \arccos \left (x \right )^{n} y+\lambda \arccos \left (x \right )^{n} \]

[_Riccati]

15.259

12166

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arccos \left (x \right )^{n} \left (x^{k +1} y-1\right ) \]

[_Riccati]

62.460

12167

\[ {}y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arccos \left (x \right )^{n} \]

[_Riccati]

15.049

12168

\[ {}y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arccos \left (x \right )^{n} y+b m \,x^{m -1} \]

[_Riccati]

70.694

12169

\[ {}y^{\prime } = \lambda \arccos \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arccos \left (x \right )^{n} \]

[_Riccati]

49.890

12170

\[ {}y^{\prime } = \lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

75.256

12171

\[ {}y^{\prime } x = \lambda \arccos \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arccos \left (x \right )^{n} \]

[_Riccati]

384.120

12172

\[ {}y^{\prime } x = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arccos \left (x \right )^{m}-n y \]

[_Riccati]

162.537

12173

\[ {}y^{\prime } = y^{2}+\lambda \arctan \left (x \right )^{n} y-a^{2}+a \lambda \arctan \left (x \right )^{n} \]

[_Riccati]

4.821

12174

\[ {}y^{\prime } = y^{2}+\lambda x \arctan \left (x \right )^{n} y+\lambda \arctan \left (x \right )^{n} \]

[_Riccati]

8.555

12175

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \arctan \left (x \right )^{n} \left (x^{k +1} y-1\right ) \]

[_Riccati]

29.351

12176

\[ {}y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \arctan \left (x \right )^{n} \]

[_Riccati]

8.446

12177

\[ {}y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}-b \lambda \,x^{m} \arctan \left (x \right )^{n} y+b m \,x^{m -1} \]

[_Riccati]

40.007

12178

\[ {}y^{\prime } = \lambda \arctan \left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \arctan \left (x \right )^{n} \]

[_Riccati]

78.468

12179

\[ {}y^{\prime } = \lambda \arctan \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

35.821

12180

\[ {}y^{\prime } x = \lambda \arctan \left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \arctan \left (x \right )^{n} \]

[_Riccati]

17.046

12181

\[ {}y^{\prime } x = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \arctan \left (x \right )^{m}-n y \]

[_Riccati]

124.711

12182

\[ {}y^{\prime } = y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} y-a^{2}+a \lambda \operatorname {arccot}\left (x \right )^{n} \]

[_Riccati]

5.084

12183

\[ {}y^{\prime } = y^{2}+\lambda x \operatorname {arccot}\left (x \right )^{n} y+\lambda \operatorname {arccot}\left (x \right )^{n} \]

[_Riccati]

11.748

12184

\[ {}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+\lambda \operatorname {arccot}\left (x \right )^{n} \left (x^{k +1} y-1\right ) \]

[_Riccati]

41.425

12185

\[ {}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+a y+a b -b^{2} \lambda \operatorname {arccot}\left (x \right )^{n} \]

[_Riccati]

11.128

12186

\[ {}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}-b \lambda \,x^{m} \operatorname {arccot}\left (x \right )^{n} y+b m \,x^{m -1} \]

[_Riccati]

84.733

12187

\[ {}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+\beta m \,x^{m -1}-\lambda \,\beta ^{2} x^{2 m} \operatorname {arccot}\left (x \right )^{n} \]

[_Riccati]

78.188

12188

\[ {}y^{\prime } = \lambda \operatorname {arccot}\left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

82.664

12189

\[ {}y^{\prime } x = \lambda \operatorname {arccot}\left (x \right )^{n} y^{2}+k y+\lambda \,b^{2} x^{2 k} \operatorname {arccot}\left (x \right )^{n} \]

[_Riccati]

36.505

12190

\[ {}y^{\prime } x = \left (a \,x^{2 m} y^{2}+b \,x^{n} y+c \right ) \operatorname {arccot}\left (x \right )^{m}-n y \]

[_Riccati]

286.000

12191

\[ {}y^{\prime } = y^{2}+f \left (x \right ) y-a^{2}-a f \left (x \right ) \]

[_Riccati]

2.102

12192

\[ {}y^{\prime } = y^{2} f \left (x \right )-a y-a b -b^{2} f \left (x \right ) \]

[_Riccati]

2.741

12193

\[ {}y^{\prime } = f \left (x \right )+x f \left (x \right ) y+y^{2} \]

[_Riccati]

2.431

12194

\[ {}y^{\prime } = y^{2} f \left (x \right )-a \,x^{n} f \left (x \right ) y+a n \,x^{n -1} \]

[_Riccati]

3.560

12195

\[ {}y^{\prime } = y^{2} f \left (x \right )+a n \,x^{n -1}-a^{2} x^{2 n} f \left (x \right ) \]

[_Riccati]

6.641

12196

\[ {}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+x^{n +1} f \left (x \right ) y-f \left (x \right ) \]

[_Riccati]

4.313

12197

\[ {}y^{\prime } x = y^{2} f \left (x \right )+n y+a \,x^{2 n} f \left (x \right ) \]

[_Riccati]

4.128

12198

\[ {}y^{\prime } x = x^{2 n} f \left (x \right ) y^{2}+\left (a \,x^{n} f \left (x \right )-n \right ) y+b f \left (x \right ) \]

[_Riccati]

8.902

12199

\[ {}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y-a^{2} f \left (x \right )-a g \left (x \right ) \]

[_Riccati]

2.758

12200

\[ {}y^{\prime } = y^{2} f \left (x \right )+g \left (x \right ) y+a n \,x^{n -1}-a \,x^{n} g \left (x \right )-a^{2} x^{2 n} f \left (x \right ) \]

[_Riccati]

187.473