2.4.23 first order ode quadrature

Table 2.1175: first order ode quadrature [386]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

1

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

[_quadrature]

1.566

2

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

[_quadrature]

1.342

3

\begin{align*} y^{\prime }&=\sqrt {x} \\ y \left (4\right ) &= 0 \\ \end{align*}

[_quadrature]

0.790

4

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

[_quadrature]

0.698

5

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

[_quadrature]

0.441

6

\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}

[_quadrature]

1.837

7

\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.458

8

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

[_quadrature]

0.461

9

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

[_quadrature]

0.527

10

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

[_quadrature]

0.447

651

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

[_quadrature]

0.476

652

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

[_quadrature]

2.231

653

\begin{align*} y^{\prime }&=\sqrt {x} \\ y \left (4\right ) &= 0 \\ \end{align*}

[_quadrature]

0.921

654

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

[_quadrature]

0.757

655

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

[_quadrature]

0.451

656

\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}

[_quadrature]

2.746

657

\begin{align*} y^{\prime }&=\frac {10}{x^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.475

658

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

[_quadrature]

0.487

659

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

[_quadrature]

0.570

660

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

[_quadrature]

0.479

1524

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

[_quadrature]

0.806

1525

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

[_quadrature]

0.412

1526

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

[_quadrature]

0.411

1527

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

[_quadrature]

0.448

1528

\begin{align*} y^{\prime }&=x \sin \left (x^{2}\right ) \\ y \left (\frac {\sqrt {2}\, \sqrt {\pi }}{2}\right ) &= 1 \\ \end{align*}

[_quadrature]

0.922

1529

\begin{align*} y^{\prime }&=\tan \left (x \right ) \\ y \left (\frac {\pi }{4}\right ) &= 3 \\ \end{align*}

[_quadrature]

0.996

2851

\begin{align*} x^{\prime }&=1-\sin \left (2 t \right ) \\ \end{align*}

[_quadrature]

0.482

3402

\begin{align*} y^{\prime }&=2 \\ \end{align*}

[_quadrature]

0.845

3403

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

[_quadrature]

0.399

3404

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

[_quadrature]

0.462

3405

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

[_quadrature]

0.490

3406

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

[_quadrature]

0.453

3407

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

[_quadrature]

0.428

3415

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

[_quadrature]

0.447

3416

\begin{align*} \sin \left (x \right ) y^{\prime }&=1 \\ \end{align*}

[_quadrature]

0.843

3417

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

[_quadrature]

0.378

3418

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

[_quadrature]

0.398

3419

\begin{align*} y^{\prime }&=\sin \left (3 t \right ) \\ \end{align*}

[_quadrature]

0.448

3420

\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ \end{align*}

[_quadrature]

0.461

3421

\begin{align*} y^{\prime }&=\frac {t}{t^{2}+4} \\ \end{align*}

[_quadrature]

0.477

3422

\begin{align*} y^{\prime }&=\ln \left (t \right ) \\ \end{align*}

[_quadrature]

0.448

3423

\begin{align*} y^{\prime }&=\frac {t}{\sqrt {t}+1} \\ \end{align*}

[_quadrature]

0.491

3427

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

[_quadrature]

0.512

3428

\begin{align*} y^{\prime }&=\sin \left (t \right )^{2} \\ y \left (\frac {\pi }{6}\right ) &= 3 \\ \end{align*}

[_quadrature]

0.591

3429

\begin{align*} y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\ y \left (0\right ) &= 12 \\ \end{align*}

[_quadrature]

0.605

3542

\begin{align*} y^{\prime }+\frac {m}{x}&=\ln \left (x \right ) \\ \end{align*}

[_quadrature]

0.363

3581

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

[_quadrature]

0.385

3582

\begin{align*} y^{\prime }&=\frac {1}{x^{{2}/{3}}} \\ \end{align*}

[_quadrature]

0.701

3585

\begin{align*} y^{\prime }&=x^{2} \ln \left (x \right ) \\ y \left (1\right ) &= 2 \\ \end{align*}

[_quadrature]

0.606

4090

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

[_quadrature]

0.377

4091

\begin{align*} y^{\prime }&=1-x^{5}+\sqrt {x} \\ \end{align*}

[_quadrature]

0.419

4105

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

[_quadrature]

0.895

4107

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

[_quadrature]

0.667

4228

\begin{align*} \left (x^{3}+1\right ) y^{\prime }&=3 \tan \left (x \right ) x^{2} \\ y \left (0\right ) &= \frac {\pi }{2} \\ \end{align*}

[_quadrature]

1.339

4386

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

[_quadrature]

181.111

4438

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

[_quadrature]

1.480

4607

\begin{align*} y^{\prime }&=a f \left (x \right ) \\ \end{align*}

[_quadrature]

0.329

4749

\begin{align*} x y^{\prime }&=\sqrt {a^{2}-x^{2}} \\ \end{align*}

[_quadrature]

1.049

4750

\begin{align*} x y^{\prime }&=-\sqrt {a^{2}-x^{2}} \\ \end{align*}

[_quadrature]

0.895

4841

\begin{align*} \left (x +a \right ) y^{\prime }&=b x \\ \end{align*}

[_quadrature]

0.581

5023

\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\ \end{align*}

[_quadrature]

1.011

5399

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

[_quadrature]

3.496

5411

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

[_quadrature]

2.253

5448

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

[_quadrature]

5.095

5487

\begin{align*} 4 {y^{\prime }}^{2} x&=\left (a -3 x \right )^{2} \\ \end{align*}

[_quadrature]

5.103

5533

\begin{align*} 4 x \left (-x +a \right ) \left (-x +b \right ) {y^{\prime }}^{2}&=\left (a b -2 x \left (a +b \right )+2 x^{2}\right )^{2} \\ \end{align*}

[_quadrature]

1.977

5537

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

[_quadrature]

5.805

5621

\begin{align*} {y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\ \end{align*}

[_quadrature]

11.629

5634

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

[_quadrature]

2.941

5685

\begin{align*} \sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }&=x \\ \end{align*}

[_quadrature]

21.381

5693

\begin{align*} a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\ \end{align*}

[_quadrature]

0.504

5694

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

[_quadrature]

0.468

5698

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

[_quadrature]

2.556

5700

\begin{align*} \ln \left (y^{\prime }\right )+x y^{\prime }+a&=0 \\ \end{align*}

[_quadrature]

6.937

6881

\begin{align*} x&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\ \end{align*}

[_quadrature]

23.694

7406

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

[_quadrature]

0.608

7695

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

[_quadrature]

0.528

7699

\begin{align*} x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \\ \end{align*}

[_quadrature]

0.672

7894

\begin{align*} 1-\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.648

8201

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

[_quadrature]

0.238

8203

\begin{align*} {y^{\prime }}^{2} x -4 y^{\prime }-12 x^{3}&=0 \\ \end{align*}

[_quadrature]

2.303

8257

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

[_quadrature]

1.095

8258

\begin{align*} y^{\prime }&=2 \\ \end{align*}

[_quadrature]

0.842

8305

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

[_quadrature]

5.529

8306

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

[_quadrature]

0.777

8338

\begin{align*} y^{\prime }&=\sin \left (5 x \right ) \\ \end{align*}

[_quadrature]

0.474

8339

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

[_quadrature]

0.425

8340

\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.543

8396

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

[_quadrature]

0.553

8681

\begin{align*} x^{\prime }+t&=1 \\ \end{align*}

[_quadrature]

0.417

8855

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

[_quadrature]

0.478

9048

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

[_quadrature]

1.580

9062

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

[_quadrature]

0.454

9063

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

[_quadrature]

0.444

9064

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

[_quadrature]

0.588

9065

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

[_quadrature]

0.523

9066

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

[_quadrature]

0.478

9067

\begin{align*} x y^{\prime }&=1 \\ \end{align*}

[_quadrature]

0.736

9068

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

[_quadrature]

0.408

9069

\begin{align*} \sin \left (x \right ) y^{\prime }&=1 \\ \end{align*}

[_quadrature]

0.944

9070

\begin{align*} \left (x^{3}+1\right ) y^{\prime }&=x \\ \end{align*}

[_quadrature]

0.800

9071

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

[_quadrature]

0.665

9072

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

[_quadrature]

0.542

9073

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

[_quadrature]

0.593

9074

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

[_quadrature]

0.725

9075

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

[_quadrature]

0.711

9076

\begin{align*} x \left (x^{2}-4\right ) y^{\prime }&=1 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

0.925

9077

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

[_quadrature]

0.842

9992

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

[_quadrature]

0.428

9993

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

[_quadrature]

1.372

9995

\begin{align*} y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.640

9996

\begin{align*} y^{\prime }&=1+\frac {\sec \left (x \right )}{x} \\ \end{align*}

[_quadrature]

0.683

10001

\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*}

[_quadrature]

0.672

10011

\begin{align*} x y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.351

10013

\begin{align*} \frac {y^{\prime }}{x}&=0 \\ \end{align*}

[_quadrature]

0.340

10014

\begin{align*} y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.329

10259

\begin{align*} y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.374

10260

\begin{align*} y^{\prime }&=a \\ \end{align*}

[_quadrature]

0.678

10261

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

[_quadrature]

0.950

10262

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

[_quadrature]

0.780

10263

\begin{align*} y^{\prime }&=a x \\ \end{align*}

[_quadrature]

0.759

10270

\begin{align*} c y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.411

10271

\begin{align*} c y^{\prime }&=a \\ \end{align*}

[_quadrature]

0.862

10272

\begin{align*} c y^{\prime }&=a x \\ \end{align*}

[_quadrature]

0.823

10289

\begin{align*} x y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.412

10290

\begin{align*} 5 y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.403

10291

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

[_quadrature]

0.436

10292

\begin{align*} \pi y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.431

10293

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

[_quadrature]

0.476

10294

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

[_quadrature]

0.493

10295

\begin{align*} x y^{\prime }&=1 \\ \end{align*}

[_quadrature]

0.611

10296

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

[_quadrature]

0.471

10297

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

[_quadrature]

0.418

10302

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

[_quadrature]

0.477

10303

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

[_quadrature]

0.396

10305

\begin{align*} {y^{\prime }}^{n}&=0 \\ \end{align*}

[_quadrature]

0.511

10306

\begin{align*} x {y^{\prime }}^{n}&=0 \\ \end{align*}

[_quadrature]

0.576

11303

\begin{align*} y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \\ \end{align*}

[_quadrature]

1.073

11389

\begin{align*} x y^{\prime }-\sqrt {a^{2}-x^{2}}&=0 \\ \end{align*}

[_quadrature]

0.638

11673

\begin{align*} {y^{\prime }}^{2}+a x y^{\prime }-b \,x^{2}-c&=0 \\ \end{align*}

[_quadrature]

32.555

11723

\begin{align*} y^{\prime }-1&=0 \\ \end{align*}

[_quadrature]

0.732

11746

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

[_quadrature]

1.439

11809

\begin{align*} {y^{\prime }}^{3}-a x y^{\prime }+x^{3}&=0 \\ \end{align*}

[_quadrature]

3.532

11852

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

[_quadrature]

0.298

11853

\begin{align*} a \cos \left (y^{\prime }\right )+b y^{\prime }+x&=0 \\ \end{align*}

[_quadrature]

0.311

11856

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

[_quadrature]

1.288

13201

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

[_quadrature]

0.245

14203

\begin{align*} x^{\prime }&=t \cos \left (t^{2}\right ) \\ x \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

1.329

14204

\begin{align*} x^{\prime }&=\frac {t +1}{\sqrt {t}} \\ x \left (1\right ) &= 4 \\ \end{align*}

[_quadrature]

0.965

14206

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

[_quadrature]

0.569

14207

\begin{align*} x^{\prime }&=\frac {1}{t \ln \left (t \right )} \\ \end{align*}

[_quadrature]

0.862

14208

\begin{align*} \sqrt {t}\, x^{\prime }&=\cos \left (\sqrt {t}\right ) \\ \end{align*}

[_quadrature]

0.794

14209

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

[_quadrature]

1.153

14871

\begin{align*} x^{\prime }&=\sin \left (t \right )+\cos \left (t \right ) \\ \end{align*}

[_quadrature]

0.654

14872

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

[_quadrature]

0.718

14873

\begin{align*} u^{\prime }&=4 t \ln \left (t \right ) \\ \end{align*}

[_quadrature]

0.940

14874

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

[_quadrature]

0.623

14875

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

[_quadrature]

0.884

14876

\begin{align*} x^{\prime }&=\sec \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

[_quadrature]

1.391

14877

\begin{align*} y^{\prime }&=x -\frac {1}{3} x^{3} \\ y \left (-1\right ) &= 1 \\ \end{align*}

[_quadrature]

0.886

14878

\begin{align*} x^{\prime }&=2 \sin \left (t \right )^{2} \\ x \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_quadrature]

0.890

14879

\begin{align*} x V^{\prime }&=x^{2}+1 \\ V \left (1\right ) &= 1 \\ \end{align*}

[_quadrature]

1.084

15494

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

[_quadrature]

0.638

15524

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

[_quadrature]

0.544

15525

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

[_quadrature]

0.557

15561

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

[_quadrature]

0.914

15570

\begin{align*} y^{\prime }&=1+3 x \\ y \left (1\right ) &= 2 \\ \end{align*}

[_quadrature]

0.782

15571

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

[_quadrature]

0.862

15572

\begin{align*} y^{\prime }&=2 \sin \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}

[_quadrature]

0.757

15573

\begin{align*} y^{\prime }&=x \sin \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 1 \\ \end{align*}

[_quadrature]

0.856

15574

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

[_quadrature]

0.841

15575

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

[_quadrature]

0.820

15576

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

[_quadrature]

0.993

15577

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

[_quadrature]

0.795

15578

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

[_quadrature]

1.704

15579

\begin{align*} y^{\prime }&=\tan \left (x \right ) \\ y \left (\pi \right ) &= 0 \\ \end{align*}

[_quadrature]

1.201

15608

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

[_quadrature]

0.762

15809

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

[_quadrature]

0.400

15810

\begin{align*} y^{\prime }&=t^{2}+1 \\ \end{align*}

[_quadrature]

0.368

15827

\begin{align*} y^{\prime }&=-t^{2}+2 \\ \end{align*}

[_quadrature]

0.400

15831

\begin{align*} y^{\prime }&=t^{2}-2 \\ \end{align*}

[_quadrature]

0.424

15833

\begin{align*} \theta ^{\prime }&=2 \\ \end{align*}

[_quadrature]

0.786

15939

\begin{align*} y^{\prime }&=t^{2} \left (t^{2}+1\right ) \\ \end{align*}

[_quadrature]

0.431

16152

\begin{align*} y^{\prime }&=3-\sin \left (x \right ) \\ \end{align*}

[_quadrature]

0.376

16155

\begin{align*} x y^{\prime }&=\arcsin \left (x^{2}\right ) \\ \end{align*}

[_quadrature]

1.668

16162

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

[_quadrature]

0.947

16163

\begin{align*} y^{\prime }&=20 \,{\mathrm e}^{-4 x} \\ \end{align*}

[_quadrature]

0.396

16164

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

[_quadrature]

0.477

16165

\begin{align*} \sqrt {x +4}\, y^{\prime }&=1 \\ \end{align*}

[_quadrature]

0.484

16166

\begin{align*} y^{\prime }&=x \cos \left (x^{2}\right ) \\ \end{align*}

[_quadrature]

0.582

16167

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

[_quadrature]

0.453

16168

\begin{align*} x&=\left (x^{2}-9\right ) y^{\prime } \\ \end{align*}

[_quadrature]

0.595

16169

\begin{align*} 1&=\left (x^{2}-9\right ) y^{\prime } \\ \end{align*}

[_quadrature]

0.578

16170

\begin{align*} 1&=x^{2}-9 y^{\prime } \\ \end{align*}

[_quadrature]

0.385

16174

\begin{align*} y^{\prime }&=40 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 4 \\ \end{align*}

[_quadrature]

0.582

16175

\begin{align*} \left (6+x \right )^{{1}/{3}} y^{\prime }&=1 \\ y \left (2\right ) &= 10 \\ \end{align*}

[_quadrature]

0.704

16176

\begin{align*} y^{\prime }&=\frac {x -1}{x +1} \\ y \left (0\right ) &= 8 \\ \end{align*}

[_quadrature]

0.559

16177

\begin{align*} x y^{\prime }+2&=\sqrt {x} \\ y \left (1\right ) &= 6 \\ \end{align*}

[_quadrature]

0.664

16178

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

[_quadrature]

1.154

16179

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

[_quadrature]

0.472

16181

\begin{align*} y^{\prime }&=\sin \left (\frac {x}{2}\right ) \\ \end{align*}

[_quadrature]

0.342

16182

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

[_quadrature]

0.441

16183

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

[_quadrature]

1.434

16184

\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ \end{align*}

[_quadrature]

0.334

16185

\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 16 \\ \end{align*}

[_quadrature]

0.506

16186

\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 20 \\ \end{align*}

[_quadrature]

0.500

16187

\begin{align*} y^{\prime }&=3 \sqrt {x +3} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

0.521

16188

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

[_quadrature]

0.438

16189

\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}+5}} \\ y \left (2\right ) &= 7 \\ \end{align*}

[_quadrature]

0.520

16190

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

[_quadrature]

0.438

16191

\begin{align*} y^{\prime }&={\mathrm e}^{-9 x^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

75.109

16192

\begin{align*} x y^{\prime }&=\sin \left (x \right ) \\ y \left (0\right ) &= 4 \\ \end{align*}

[_quadrature]

0.666

16193

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

[_quadrature]

0.657

16194

\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.242

16195

\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*}

[_quadrature]

0.233

16196

\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.254

16211

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

[_quadrature]

0.417

16262

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

[_quadrature]

0.338

16336

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

[_quadrature]

0.435

16347

\begin{align*} \left (x^{2}-4\right ) y^{\prime }&=x \\ \end{align*}

[_quadrature]

0.593

16352

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

[_quadrature]

0.755

16363

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

[_quadrature]

0.536

16373

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

[_quadrature]

0.398

16961

\begin{align*} 2 x -1-y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.386

16980

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

[_quadrature]

0.671

16981

\begin{align*} y^{\prime }&=x \sin \left (x^{2}\right ) \\ \end{align*}

[_quadrature]

0.618

16982

\begin{align*} y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\ \end{align*}

[_quadrature]

0.379

16983

\begin{align*} y^{\prime }&=\frac {1}{x \ln \left (x \right )} \\ \end{align*}

[_quadrature]

0.570

16984

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

[_quadrature]

0.489

16985

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

[_quadrature]

0.389

16986

\begin{align*} y^{\prime }&=\frac {-10-2 x}{\left (x +2\right ) \left (x -4\right )} \\ \end{align*}

[_quadrature]

0.530

16987

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

[_quadrature]

0.530

16988

\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}-16}}{x} \\ \end{align*}

[_quadrature]

0.453

16989

\begin{align*} y^{\prime }&=\left (-x^{2}+4\right )^{{3}/{2}} \\ \end{align*}

[_quadrature]

0.519

16990

\begin{align*} y^{\prime }&=\frac {1}{x^{2}-16} \\ \end{align*}

[_quadrature]

0.559

16991

\begin{align*} y^{\prime }&=\cos \left (x \right ) \cot \left (x \right ) \\ \end{align*}

[_quadrature]

0.969

16992

\begin{align*} y^{\prime }&=\sin \left (x \right )^{3} \tan \left (x \right ) \\ \end{align*}

[_quadrature]

0.888

17001

\begin{align*} y^{\prime }&=4 x^{3}-x +2 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

0.513

17002

\begin{align*} y^{\prime }&=\sin \left (2 t \right )-\cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.645

17003

\begin{align*} y^{\prime }&=\frac {\cos \left (\frac {1}{x}\right )}{x^{2}} \\ y \left (\frac {2}{\pi }\right ) &= 1 \\ \end{align*}

[_quadrature]

0.724

17004

\begin{align*} y^{\prime }&=\frac {\ln \left (x \right )}{x} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

0.648

17011

\begin{align*} y^{\prime }&=\sin \left (x \right )^{4} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.818

17025

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

[_quadrature]

0.365

17026

\begin{align*} y^{\prime }&=x^{2} \sin \left (x \right ) \\ \end{align*}

[_quadrature]

0.531

17027

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

[_quadrature]

0.523

17028

\begin{align*} y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\ \end{align*}

[_quadrature]

0.629

17032

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

[_quadrature]

0.534

17033

\begin{align*} y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.674

17044

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

[_quadrature]

0.450

17107

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

[_quadrature]

9.527

17108

\begin{align*} y^{\prime }&=\cos \left (t \right ) \\ y \left (\frac {\pi }{2}\right ) &= -1 \\ \end{align*}

[_quadrature]

0.513

17110

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

[_quadrature]

0.523

17116

\begin{align*} y^{\prime }&=t \sin \left (t^{2}\right ) \\ y \left (\sqrt {\pi }\right ) &= 0 \\ \end{align*}

[_quadrature]

0.980

17117

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

[_quadrature]

0.463

17206

\begin{align*} 3 t^{2}-y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.813

17851

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

[_quadrature]

0.426

17863

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

[_quadrature]

0.418

17867

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

[_quadrature]

1.010

17868

\begin{align*} y^{\prime }&=\frac {1}{x} \\ \end{align*}

[_quadrature]

0.714

17895

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

[_quadrature]

1.408

17896

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

[_quadrature]

0.765

17897

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

[_quadrature]

0.550

17898

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

[_quadrature]

1.171

17899

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

[_quadrature]

0.796

17900

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

[_quadrature]

0.478

17901

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

[_quadrature]

0.440

18001

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

[_quadrature]

9.419

18008

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

[_quadrature]

0.372

18049

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

[_quadrature]

0.737

18625

\begin{align*} x y^{\prime }&=-\frac {1}{\ln \left (x \right )} \\ \end{align*}

[_quadrature]

0.993

19063

\begin{align*} y^{\prime }&=2 \\ \end{align*}

[_quadrature]

0.776

19064

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

[_quadrature]

0.668

19227

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

[_quadrature]

1.030

19241

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

[_quadrature]

0.450

19242

\begin{align*} x y^{\prime }&=1 \\ \end{align*}

[_quadrature]

0.648

19243

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

[_quadrature]

0.422

19244

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

[_quadrature]

0.401

19245

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

[_quadrature]

0.537

19246

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

[_quadrature]

0.494

19247

\begin{align*} \left (x^{3}+1\right ) y^{\prime }&=x \\ \end{align*}

[_quadrature]

0.726

19248

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

[_quadrature]

0.438

19254

\begin{align*} \sin \left (x \right ) y^{\prime }&=1 \\ \end{align*}

[_quadrature]

0.784

19259

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

[_quadrature]

0.524

19260

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

[_quadrature]

0.562

19261

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

[_quadrature]

0.591

19262

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

[_quadrature]

0.730

19263

\begin{align*} x \left (x^{2}-4\right ) y^{\prime }&=1 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

0.837

19264

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

[_quadrature]

1.157

19266

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

[_quadrature]

0.711

19269

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

[_quadrature]

0.770

19659

\begin{align*} x^{\prime }&=3 t^{2}+4 t \\ x \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

0.562

19660

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

[_quadrature]

0.349

19661

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

[_quadrature]

0.477

19662

\begin{align*} x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}} \\ x \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

0.536

19663

\begin{align*} x^{\prime }&=\cos \left (t \right ) \\ x \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

0.517

19664

\begin{align*} x^{\prime }&=\frac {\cos \left (t \right )}{\sin \left (t \right )} \\ x \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

1.165

19732

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

[_quadrature]

0.303

19737

\begin{align*} \sec \left (\theta \right )^{2}&=\frac {m s^{\prime }}{k} \\ \end{align*}

[_quadrature]

0.339

19744

\begin{align*} \sqrt {1+v^{\prime }}&=\frac {{\mathrm e}^{u}}{2} \\ \end{align*}

[_quadrature]

0.481

20007

\begin{align*} x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\ \end{align*}

[_quadrature]

0.336

20023

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

[_quadrature]

1.337

20032

\begin{align*} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\ \end{align*}

[_quadrature]

1.139

20385

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

[_quadrature]

1.049

20425

\begin{align*} x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}}&=a \\ \end{align*}

[_quadrature]

0.679

20456

\begin{align*} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\ \end{align*}

[_quadrature]

1.453

20457

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=\frac {12 {y^{\prime }}^{2}}{x} \\ \end{align*}

[_quadrature]

53.995

20462

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

[_quadrature]

1.688

20720

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

[_quadrature]

1.303

20737

\begin{align*} 4 {y^{\prime }}^{2} x&=\left (3 x -a \right )^{2} \\ \end{align*}

[_quadrature]

2.270

20738

\begin{align*} 4 {y^{\prime }}^{2} x \left (x -a \right ) \left (x -b \right )&=\left (3 x^{2}-2 x \left (a +b \right )+a b \right )^{2} \\ \end{align*}

[_quadrature]

0.660

21339

\begin{align*} \sqrt {x}\, y^{\prime }+1&=0 \\ \end{align*}

[_quadrature]

2.099

21381

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

[_quadrature]

1.314

21473

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

[_quadrature]

9.217

21800

\begin{align*} x^{3} y^{\prime }-x^{3}&=1 \\ \end{align*}

[_quadrature]

0.655

21974

\begin{align*} y^{\prime }&=5 \\ \end{align*}

[_quadrature]

1.378

21999

\begin{align*} \frac {1}{x}+y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.924

22072

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

[_quadrature]

0.422

22304

\begin{align*} y^{\prime }&=3 \sin \left (x \right ) \\ y \left (\pi \right ) &= -1 \\ \end{align*}

[_quadrature]

0.727

22305

\begin{align*} x^{\prime }&=4 \,{\mathrm e}^{-t}-2 \\ x \left (0\right ) &= 3 \\ \end{align*}

[_quadrature]

0.672

22307

\begin{align*} s^{\prime }&=9 \sqrt {u} \\ s \left (4\right ) &= 16 \\ \end{align*}

[_quadrature]

1.663

22309

\begin{align*} y^{\prime }&=-\frac {4}{x^{2}} \\ y \left (1\right ) &= 2 \\ \end{align*}

[_quadrature]

1.351

22351

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

[_quadrature]

2.109

22419

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

[_quadrature]

1.118

22513

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

[_quadrature]

0.536

23055

\begin{align*} r^{\prime }&=-a \sin \left (\theta \right ) \\ r \left (0\right ) &= 2 a \\ \end{align*}

[_quadrature]

0.281

23061

\begin{align*} \sin \left (\theta \right )^{2} r^{\prime }&=-b \cos \left (\theta \right ) \\ \end{align*}

[_quadrature]

0.384

23062

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

[_quadrature]

0.359

23063

\begin{align*} r^{\prime }&=c \\ r \left (0\right ) &= a \\ \end{align*}

[_quadrature]

0.605

23258

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

[_quadrature]

0.411

23828

\begin{align*} y^{\prime }&=\frac {1}{t^{2}} \\ \end{align*}

[_quadrature]

0.727

23829

\begin{align*} y^{\prime }&=\cos \left (t \right )^{2} \\ \end{align*}

[_quadrature]

0.414

23830

\begin{align*} y^{\prime }&=\frac {1}{t^{2}-1} \\ \end{align*}

[_quadrature]

0.476

23831

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

[_quadrature]

0.394

23832

\begin{align*} y^{\prime }&=\frac {1}{\sqrt {t^{2}+2 t}} \\ \end{align*}

[_quadrature]

0.540

23833

\begin{align*} y^{\prime }&=t \ln \left (t \right ) \\ \end{align*}

[_quadrature]

0.413

23834

\begin{align*} y^{\prime }&=\frac {t^{2}+1}{t \left (t -2\right )} \\ \end{align*}

[_quadrature]

0.501

23839

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

[_quadrature]

0.411

24139

\begin{align*} x -\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.642

24140

\begin{align*} x +\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.477

24141

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

[_quadrature]

1.067

24259

\begin{align*} \left (x +a \right ) y^{\prime }&=b x \\ \end{align*}

[_quadrature]

0.475

24922

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

[_quadrature]

0.394

24923

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

[_quadrature]

0.401

24924

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

[_quadrature]

0.425

24925

\begin{align*} y^{\prime }&=\frac {t +1}{t} \\ \end{align*}

[_quadrature]

0.480

24932

\begin{align*} y^{\prime }&={\mathrm e}^{2 t}-1 \\ y \left (0\right ) &= 4 \\ \end{align*}

[_quadrature]

0.505

24933

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

[_quadrature]

0.518

24935

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

[_quadrature]

1.442

25041

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

[_quadrature]

0.559

25403

\begin{align*} y^{\prime }&=5 \\ y \left (0\right ) &= 2 \\ \end{align*}

[_quadrature]

1.761

25413

\begin{align*} y^{\prime }&=\operatorname {Heaviside}\left (t -T \right ) \\ y \left (0\right ) &= 2 \\ \end{align*}

[_quadrature]

1.260

25417

\begin{align*} y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\operatorname {Heaviside}\left (t -2\right )+\operatorname {Heaviside}\left (-3+t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.911

25422

\begin{align*} y^{\prime }&=\operatorname {Heaviside}\left (t -1\right )+\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.793

25442

\begin{align*} y^{\prime }&=A \cos \left (\omega t \right )+B \sin \left (\omega t \right ) \\ \end{align*}

[_quadrature]

0.398

25647

\begin{align*} y^{\prime }&=2 \,{\mathrm e}^{2 t}-4 \,{\mathrm e}^{t} \\ \end{align*}

[_quadrature]

0.516

25783

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

[_quadrature]

10.871

25784

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

[_quadrature]

0.940

25805

\begin{align*} y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.641

25815

\begin{align*} y^{\prime }&=\sin \left (5 x \right ) \\ \end{align*}

[_quadrature]

0.485

25816

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

[_quadrature]

0.473

25817

\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}

[_quadrature]

0.658

25831

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

[_quadrature]

2.103

25834

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

[_quadrature]

1.989

26130

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

[_quadrature]

2.088

26156

\begin{align*} y^{\prime } \ln \left (\frac {y^{\prime }}{4}\right )&=4 x \\ \end{align*}

[_quadrature]

0.446

26157

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

[_quadrature]

1.989

26158

\begin{align*} x&=y^{\prime }+\arcsin \left (y^{\prime }\right ) \\ \end{align*}

[_quadrature]

0.730

26159

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

[_quadrature]

0.260

26184

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

[_quadrature]

0.344

26196

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

[_quadrature]

0.342

26241

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

[_quadrature]

0.644

26242

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

[_quadrature]

0.404

26243

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

[_quadrature]

0.241

26244

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

[_quadrature]

0.312

26245

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

[_quadrature]

0.438

26246

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

[_quadrature]

0.217

26247

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

[_quadrature]

0.273

26354

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

[_quadrature]

2.934

26364

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

[_quadrature]

0.289

26389

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

[_quadrature]

0.561

26754

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

[_quadrature]

0.481

26923

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

[_quadrature]

0.904

26924

\begin{align*} y^{\prime }&=\cos \left (x \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}

[_quadrature]

0.503

27378

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

[_quadrature]

1072.464

27379

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

[_quadrature]

1.217

27465

\begin{align*} 2 y^{\prime }&=x +\ln \left (y^{\prime }\right ) \\ \end{align*}

[_quadrature]

1.974