2.4.29 first order ode special form ID 1

Table 2.1107: first order ode special form ID 1 [74]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

67

\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

1.580

702

\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.120

1184

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

[_quadrature]

0.833

1185

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

[_quadrature]

0.829

1237

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

[_separable]

1.374

2320

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

[_separable]

1.342

2491

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

[_separable]

1.388

2864

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

[_quadrature]

0.730

3410

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

[_separable]

3.345

4094

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

[_separable]

1.654

4101

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

[_separable]

1.784

4104

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

[_separable]

2.053

4214

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

[_separable]

1.473

4215

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

[_separable]

1.221

4225

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

[_separable]

3.191

4434

\begin{align*} y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

2.987

4734

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

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

1.355

4735

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

[_separable]

1.149

7039

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

[_separable]

2.468

7403

\begin{align*} y^{\prime }&=8 x^{3} {\mathrm e}^{-2 y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

2.917

7741

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

[_separable]

3.309

8315

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

[_separable]

2.122

8316

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}

[_separable]

2.171

8344

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

[_separable]

1.507

8371

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

[_separable]

3.065

8374

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

[_separable]

1.939

8677

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

[_separable]

1.766

9009

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x -y}}{{\mathrm e}^{x}+1} \\ \end{align*}

[_separable]

1.643

10256

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

[_separable]

2.258

10324

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

[_separable]

1.369

10325

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

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

1.161

10326

\begin{align*} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \\ \end{align*}

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

1.714

10327

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

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

2.326

10328

\begin{align*} y^{\prime }&=5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \\ \end{align*}

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

2.231

11376

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

[_separable]

2.113

14196

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

[_quadrature]

0.401

14212

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

[_quadrature]

3.033

14228

\begin{align*} x^{\prime }&=t^{2} {\mathrm e}^{-x} \\ x \left (0\right ) &= \ln \left (2\right ) \\ \end{align*}

[_separable]

6.002

14230

\begin{align*} x^{\prime }&={\mathrm e}^{t +x} \\ x \left (0\right ) &= 0 \\ \end{align*}

[_separable]

5.367

15022

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

[_separable]

1.997

15542

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

[_separable]

1.534

15583

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

[_separable]

2.119

15588

\begin{align*} x \,{\mathrm e}^{y}+y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.365

15779

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

[_quadrature]

0.596

16223

\begin{align*} y^{\prime }&={\mathrm e}^{2 x -3 y} \\ \end{align*}

[_separable]

1.641

16242

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

[_quadrature]

0.441

16243

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

[_quadrature]

0.645

16376

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

[_separable]

1.516

16378

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

[_separable]

1.205

17082

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \\ \end{align*}

[_separable]

1.685

17083

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

[_separable]

1.709

17114

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

[_separable]

5.777

17120

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

[_separable]

2.434

17121

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

[_separable]

2.753

17313

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\ \end{align*}

[_separable]

2.441

18065

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

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

1.182

18492

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

[_separable]

3.505

19265

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

[_separable]

6.729

19267

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

[_separable]

4.392

19666

\begin{align*} x^{\prime }&=b \,{\mathrm e}^{x} \\ x \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

1.977

20282

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

[_separable]

2.717

20317

\begin{align*} s^{\prime }+x^{2}&=x^{2} {\mathrm e}^{3 s} \\ \end{align*}

[_separable]

2.311

21045

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

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

2.340

22323

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

[_quadrature]

0.605

22599

\begin{align*} y^{\prime }&={\mathrm e}^{x +3 y}+1 \\ \end{align*}

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

1.054

24148

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

[_separable]

3.960

24268

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

[_separable]

1.829

24327

\begin{align*} y^{\prime }&=1+6 x \,{\mathrm e}^{x -y} \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

3.226

24919

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

[_quadrature]

0.764

25027

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

[_quadrature]

0.473

25498

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

[_separable]

1.850

25793

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

[_separable]

3.469

25794

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y} \\ y \left (1\right ) &= {\frac {5}{2}} \\ \end{align*}

[_separable]

3.524

25821

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

[_separable]

1.455