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]

8.904

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]

75.075

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]

35.529

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]

23.368

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]

65.945

12106

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

[_Riccati]

24.529

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]

129.015

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]

6.187

12109

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

[_Riccati]

3.066

12110

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

[_Riccati]

6.966

12111

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

[_Riccati]

164.896

12112

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

[_Riccati]

4.738

12113

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

[_Riccati]

17.932

12114

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

[_Riccati]

19.305

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]

47.310

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]

33.838

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]

19.200

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]

40.479

12119

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

[_Riccati]

52.175

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]

126.967

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]

5.943

12122

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

[_Riccati]

6.471

12123

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

[_Riccati]

6.878

12124

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

[_Riccati]

5.879

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]

11.008

12126

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

[_Riccati]

5.615

12127

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

[_Riccati]

6.640

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]

15.312

12129

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

[_Riccati]

40.461

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]

175.727

12131

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

[_Riccati]

58.038

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]

214.495

12133

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

[_Riccati]

6.197

12134

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

[_Riccati]

6.226

12135

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

[_Riccati]

8.385

12136

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

[_Riccati]

6.626

12137

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

[_Riccati]

7.033

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]

15.511

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]

201.072

12140

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

[_Riccati]

67.478

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]

240.612

12142

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

[_Riccati]

31.267

12143

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

[_Riccati]

13.618

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]

55.721

12145

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

[_Riccati]

15.604

12146

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

[_Riccati]

17.170

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]

380.894

12148

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

[_Riccati]

7.004

12149

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

[_Riccati]

35.551

12150

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

[_Riccati]

35.622

12151

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

[_Riccati]

114.721

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]

18.017

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]

38.778

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]

13.905

12155

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

[_Riccati]

4.063

12156

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

[_Riccati]

7.141

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]

55.960

12158

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

[_Riccati]

10.940

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]

32.869

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]

46.053

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]

36.481

12162

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

[_Riccati]

28.971

12163

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

[_Riccati]

114.635

12164

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

[_Riccati]

9.006

12165

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

[_Riccati]

16.732

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]

64.711

12167

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

[_Riccati]

15.878

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]

72.799

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]

51.037

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]

42.964

12171

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

[_Riccati]

93.248

12172

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

[_Riccati]

157.086

12173

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

[_Riccati]

5.015

12174

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

[_Riccati]

6.702

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]

39.888

12176

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

[_Riccati]

9.604

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]

53.950

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]

95.970

12180

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

[_Riccati]

36.209

12181

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

[_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]

5.320

12183

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

[_Riccati]

10.922

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]

43.375

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]

12.811

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]

102.496

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]

115.681

12189

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

[_Riccati]

36.863

12190

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

[_Riccati]

286.000

12191

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

[_Riccati]

1.743

12192

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

[_Riccati]

2.427

12193

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

[_Riccati]

1.753

12194

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

[_Riccati]

3.392

12195

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

[_Riccati]

6.403

12196

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

[_Riccati]

3.111

12197

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

[_Riccati]

3.334

12198

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

[_Riccati]

17.440

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]

2.468

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]

149.789