2.4.31 first order ode special form ID 1

Table 2.1211: first order ode special form ID 1 [81]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

67

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=6 \,{\mathrm e}^{2 x -y}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

17.894

702

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=6 \,{\mathrm e}^{2 x -y}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

674.479

1184

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-1+{\mathrm e}^{y} \end {array} \]

[_quadrature]

135.855

1185

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-1+{\mathrm e}^{-y} \end {array} \]

[_quadrature]

133.242

1237

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]

[_separable]

195.171

2320

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3+t +y} \end {array} \]

[_separable]

70.473

2491

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3+t +y} \end {array} \]

[_separable]

96.905

2864

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y}\\ y \left (0\right )&=0\\ \end {array} \]

[_quadrature]

145.029

3410

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-x \,{\mathrm e}^{y} \end {array} \]

[_separable]

502.840

4094

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{2 y}+\left (x +1\right ) y^{\prime }&=0 \end {array} \]

[_separable]

3.501

4101

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -2 y}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

96.796

4104

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

86.770

4214

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y} \sin \left (x \right ) \end {array} \]

[_separable]

95.716

4215

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]

[_separable]

125.106

4225

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{-2 y}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

84.046

4434

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \end {array} \]

[[_1st_order, _with_linear_symmetries]]

219.378

4734

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y}+x \end {array} \]

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

57.297

4735

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]

[_separable]

57.004

7039

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \end {array} \]

[_separable]

84.254

7403

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y}\\ y \left (1\right )&=0\\ \end {array} \]

[_separable]

251.678

7741

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 x -2 y}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

2.607

8315

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{y}\\ y \left (0\right )&=-2\\ \end {array} \]

[_separable]

728.295

8316

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{y}\\ y \left (1\right )&={\frac {5}{2}}\\ \end {array} \]

[_separable]

693.509

8344

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 x +2 y} \end {array} \]

[_separable]

138.941

8371

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{-2 y} \sin \left (x \right )}{x^{2}+1}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

81.665

8374

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{y}-{\mathrm e}^{-x} y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

104.746

8677

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]

[_separable]

163.470

9009

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{{\mathrm e}^{x}+1} \end {array} \]

[_separable]

112.218

10256

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+{\mathrm e}^{-y}&=0 \end {array} \]

[_separable]

189.057

10324

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]

[_separable]

43.245

10325

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=10+{\mathrm e}^{x +y} \end {array} \]

[[_homogeneous, ‘class C‘], _dAlembert]

44.083

10326

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \end {array} \]

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

44.089

10327

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \end {array} \]

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

38.118

10328

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \end {array} \]

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

73.699

11376

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \end {array} \]

[_separable]

86.013

14196

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{-x} \end {array} \]

[_quadrature]

76.777

14212

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{-2 x}\\ x \left (0\right )&=1\\ \end {array} \]

[_quadrature]

80.996

14228

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=t^{2} {\mathrm e}^{-x}\\ x \left (0\right )&=\ln \left (2\right )\\ \end {array} \]

[_separable]

277.877

14230

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{t +x}\\ x \left (0\right )&=0\\ \end {array} \]

[_separable]

87.128

15022

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]

[_separable]

246.899

15542

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]

[_separable]

341.639

15583

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{-x^{2}+y}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

1496.005

15588

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \,{\mathrm e}^{y}+y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

1837.459

15779

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{-y} \end {array} \]

[_quadrature]

381.659

16223

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{2 x -3 y} \end {array} \]

[_separable]

364.022

16242

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{-y} \end {array} \]

[_quadrature]

212.990

16243

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{-y}+1 \end {array} \]

[_quadrature]

211.819

16376

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{4 x +3 y} \end {array} \]

[_separable]

547.013

16378

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{4 x +3 y} \end {array} \]

[_separable]

555.016

17082

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{2 y+10 t} \end {array} \]

[_separable]

326.584

17083

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 y+2 t} \end {array} \]

[_separable]

204.990

17114

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{t -y}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

186.207

17120

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y}\\ y \left (0\right )&=1\\ \end {array} \]

[_separable]

140.962

17121

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{2 x -y}\\ y \left (0\right )&=1\\ \end {array} \]

[_separable]

78.604

17313

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \end {array} \]

[_separable]

289.562

18065

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-1&={\mathrm e}^{x +2 y} \end {array} \]

[[_homogeneous, ‘class C‘], _dAlembert]

2.329

18492

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2} {\mathrm e}^{-3 y}\\ y \left (2\right )&=0\\ \end {array} \]

[_separable]

8.269

19265

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 x -2 y}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

149.299

19267

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }&=0\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

83.783

19666

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=b \,{\mathrm e}^{x}\\ x \left (0\right )&=1\\ \end {array} \]

[_quadrature]

1.916

20282

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y^{\prime }&=x \,{\mathrm e}^{\left (n -1\right ) y} \end {array} \]

[_separable]

7.195

20317

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \end {array} \]

[_separable]

266.608

21045

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&={\mathrm e}^{x}-t \end {array} \]

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

2.339

22323

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y}\\ y \left (1\right )&=0\\ \end {array} \]

[_quadrature]

42.447

22599

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +3 y}+1 \end {array} \]

[[_homogeneous, ‘class C‘], _dAlembert]

135.454

24148

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}}\\ y \left (0\right )&=0\\ \end {array} \]

[_separable]

1078.774

24268

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]

[_separable]

97.575

24327

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+6 x \,{\mathrm e}^{x -y} \end {array} \]

[[_1st_order, _with_linear_symmetries]]

129.383

24919

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-{\mathrm e}^{y}-1 \end {array} \]

[_quadrature]

116.726

25027

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-{\mathrm e}^{y} \end {array} \]

[_quadrature]

166.316

25498

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{y+t} \end {array} \]

[_separable]

229.632

25793

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{y}\\ y \left (0\right )&=-2\\ \end {array} \]

[_separable]

1323.869

25794

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{y}\\ y \left (1\right )&={\frac {5}{2}}\\ \end {array} \]

[_separable]

1262.563

25821

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{3 x +2 y} \end {array} \]

[_separable]

428.239

26080

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{3 y} \sin \left (x \right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \end {array} \]

[_separable]

263.860

26162

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x -y} \end {array} \]

[_separable]

271.575

26407

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-1&={\mathrm e}^{x +2 y} \end {array} \]

[[_homogeneous, ‘class C‘], _dAlembert]

151.922

27428

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&={\mathrm e}^{y}+2 y^{\prime } \end {array} \]

[_separable]

3.301

28039

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \,{\mathrm e}^{-y} \end {array} \]

[_separable]

4.740

28047

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime }+{\mathrm e}^{t +z}&=0 \end {array} \]

[_separable]

8.691

28128

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x^{2} {\mathrm e}^{y}\\ y \left (0\right )&=1\\ \end {array} \]

[_separable]

6.165