2.4.31 first order ode special form ID 1

Table 2.1191: first order ode special form ID 1 [78]

#

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]

3.409

702

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

[_separable]

2.586

1184

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

[_quadrature]

1.703

1185

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

[_quadrature]

1.668

1237

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

[_separable]

2.029

2320

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

[_separable]

2.540

2491

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

[_separable]

2.835

2864

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

[_quadrature]

1.231

3410

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

[_separable]

2.993

4094

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

[_separable]

2.960

4101

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

[_separable]

4.306

4104

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

[_separable]

3.531

4214

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

[_separable]

2.965

4215

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

[_separable]

3.295

4225

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

[_separable]

5.264

4434

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

[[_1st_order, _with_linear_symmetries]]

5.652

4734

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

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

2.898

4735

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

[_separable]

4.028

7039

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

[_separable]

2.307

7403

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

[_separable]

3.530

7741

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

[_separable]

3.526

8315

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

[_separable]

3.951

8316

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

[_separable]

4.189

8344

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

[_separable]

3.201

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]

4.175

8374

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

[_separable]

3.788

8677

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

[_separable]

3.388

9009

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

[_separable]

2.989

10256

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

[_separable]

3.288

10324

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

[_separable]

2.362

10325

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

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

2.069

10326

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

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

2.180

10327

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

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

2.802

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)]‘]]

2.634

11376

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

[_separable]

3.374

14196

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

[_quadrature]

1.599

14212

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

[_quadrature]

3.075

14228

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

[_separable]

8.334

14230

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

[_separable]

7.116

15022

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

[_separable]

5.672

15542

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

[_separable]

5.851

15583

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

[_separable]

4.401

15588

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

[_separable]

7.596

15779

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

[_quadrature]

1.007

16223

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

[_separable]

2.578

16242

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

[_quadrature]

1.041

16243

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

[_quadrature]

1.530

16376

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

[_separable]

2.904

16378

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

[_separable]

2.385

17082

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

[_separable]

3.556

17083

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

[_separable]

3.493

17114

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

[_separable]

16.835

17120

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

[_separable]

4.913

17121

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

[_separable]

5.405

17313

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

[_separable]

4.041

18065

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

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

4.449

18492

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

[_separable]

8.095

19265

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

[_separable]

3.791

19267

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

[_separable]

3.043

19666

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

[_quadrature]

0.957

20282

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

[_separable]

5.003

20317

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

[_separable]

3.134

21045

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

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

2.711

22323

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

[_quadrature]

1.364

22599

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

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

7.787

24148

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

[_separable]

2.497

24268

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

[_separable]

3.276

24327

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

[[_1st_order, _with_linear_symmetries]]

5.177

24919

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

[_quadrature]

3.108

25027

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

[_quadrature]

1.345

25498

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

[_separable]

4.407

25793

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

[_separable]

6.059

25794

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

[_separable]

6.238

25821

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

[_separable]

5.145

26080

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

[_separable]

3.844

26162

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

[_separable]

1.730

26407

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

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

2.080

27428

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

[_separable]

3.757