2.4.23 first order ode quadrature

Table 2.1175: first order ode quadrature [385]

#

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]

0.588

2

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

[_quadrature]

1.377

3

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

[_quadrature]

0.840

4

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

[_quadrature]

0.736

5

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

[_quadrature]

0.468

6

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

[_quadrature]

0.796

7

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

[_quadrature]

0.479

8

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

[_quadrature]

0.480

9

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

[_quadrature]

0.579

10

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

[_quadrature]

0.461

651

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

[_quadrature]

0.434

652

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

[_quadrature]

0.494

653

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

[_quadrature]

0.741

654

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

[_quadrature]

0.688

655

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

[_quadrature]

0.496

656

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

[_quadrature]

0.526

657

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

[_quadrature]

0.474

658

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

[_quadrature]

0.538

659

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

[_quadrature]

0.542

660

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

[_quadrature]

0.533

1524

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

[_quadrature]

0.977

1525

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

[_quadrature]

0.498

1526

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

[_quadrature]

0.466

1527

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

[_quadrature]

0.525

1528

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

[_quadrature]

1.025

1529

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

[_quadrature]

1.096

2851

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

[_quadrature]

0.442

3402

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

[_quadrature]

1.104

3403

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

[_quadrature]

0.441

3404

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

[_quadrature]

0.525

3405

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

[_quadrature]

0.517

3406

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

[_quadrature]

0.460

3407

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

[_quadrature]

0.439

3415

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

[_quadrature]

0.467

3416

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

[_quadrature]

0.860

3417

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

[_quadrature]

0.437

3418

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

[_quadrature]

0.443

3419

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

[_quadrature]

0.457

3420

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

[_quadrature]

0.462

3421

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

[_quadrature]

0.446

3422

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

[_quadrature]

0.484

3423

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

[_quadrature]

0.535

3427

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

[_quadrature]

0.575

3428

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

[_quadrature]

0.589

3429

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

[_quadrature]

0.595

3542

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

[_quadrature]

0.435

3581

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

[_quadrature]

0.450

3582

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

[_quadrature]

0.972

3585

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

[_quadrature]

0.687

4090

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

[_quadrature]

0.372

4091

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

[_quadrature]

0.465

4105

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

[_quadrature]

0.806

4107

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

[_quadrature]

0.497

4228

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

[_quadrature]

1.160

4386

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

[_quadrature]

6.626

4438

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

[_quadrature]

1.139

4607

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

[_quadrature]

0.296

4749

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

[_quadrature]

0.618

4750

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

[_quadrature]

0.401

4841

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

[_quadrature]

0.393

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]

0.884

5399

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

[_quadrature]

2.667

5411

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

[_quadrature]

1.672

5448

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

[_quadrature]

4.027

5487

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

[_quadrature]

4.033

5533

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

[_quadrature]

1.428

5537

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

[_quadrature]

3.475

5621

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

[_quadrature]

9.068

5634

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

[_quadrature]

2.335

5685

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

[_quadrature]

17.362

5693

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

[_quadrature]

0.473

5694

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

[_quadrature]

0.455

5698

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

[_quadrature]

2.240

5700

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

[_quadrature]

5.543

6881

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

[_quadrature]

19.993

7406

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

[_quadrature]

1.142

7695

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

[_quadrature]

0.797

7699

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

[_quadrature]

1.012

7894

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

[_quadrature]

1.607

8201

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

[_quadrature]

0.461

8203

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

[_quadrature]

5.723

8257

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

[_quadrature]

3.253

8258

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

[_quadrature]

1.976

8305

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

[_quadrature]

33.618

8306

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

[_quadrature]

2.362

8338

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

[_quadrature]

0.726

8339

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

[_quadrature]

0.639

8340

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

[_quadrature]

1.105

8396

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

[_quadrature]

0.875

8681

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

[_quadrature]

0.796

8855

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

[_quadrature]

0.807

9048

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

[_quadrature]

3.887

9062

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

[_quadrature]

0.741

9063

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

[_quadrature]

0.651

9064

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

[_quadrature]

0.760

9065

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

[_quadrature]

0.760

9066

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

[_quadrature]

0.963

9067

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

[_quadrature]

1.083

9068

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

[_quadrature]

0.618

9069

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

[_quadrature]

1.607

9070

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

[_quadrature]

0.904

9071

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

[_quadrature]

0.852

9072

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

[_quadrature]

0.838

9073

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

[_quadrature]

1.092

9074

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

[_quadrature]

1.187

9075

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

[_quadrature]

1.023

9076

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

[_quadrature]

1.205

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]

1.845

9992

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

[_quadrature]

0.665

9993

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

[_quadrature]

2.970

9995

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

[_quadrature]

1.366

9996

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

[_quadrature]

1.027

10001

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

[_quadrature]

1.075

10011

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

[_quadrature]

1.764

10013

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

[_quadrature]

1.404

10014

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

[_quadrature]

1.369

10259

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

[_quadrature]

1.457

10260

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

[_quadrature]

4.047

10261

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

[_quadrature]

4.059

10262

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

[_quadrature]

2.203

10263

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

[_quadrature]

1.358

10270

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

[_quadrature]

2.091

10271

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

[_quadrature]

5.100

10272

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

[_quadrature]

3.858

10289

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

[_quadrature]

1.890

10290

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

[_quadrature]

1.888

10291

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

[_quadrature]

1.914

10292

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

[_quadrature]

1.898

10293

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

[_quadrature]

2.348

10294

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

[_quadrature]

2.493

10295

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

[_quadrature]

1.177

10296

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

[_quadrature]

0.812

10297

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

[_quadrature]

1.892

10302

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

[_quadrature]

2.340

10303

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

[_quadrature]

1.625

10305

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

[_quadrature]

1.887

10306

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

[_quadrature]

2.926

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]

1.166

11389

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

[_quadrature]

0.479

11673

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

[_quadrature]

27.936

11723

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

[_quadrature]

0.964

11746

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

[_quadrature]

2.006

11809

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

[_quadrature]

5.401

11852

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

[_quadrature]

0.358

11853

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

[_quadrature]

0.371

11856

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

[_quadrature]

1.352

13201

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

[_quadrature]

0.661

14203

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

[_quadrature]

1.491

14204

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

[_quadrature]

1.359

14206

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

[_quadrature]

0.618

14207

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

[_quadrature]

0.955

14208

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

[_quadrature]

1.054

14209

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

[_quadrature]

1.508

14871

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

[_quadrature]

0.707

14872

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

[_quadrature]

0.752

14873

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

[_quadrature]

0.921

14874

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

[_quadrature]

0.683

14875

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

[_quadrature]

0.940

14876

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

[_quadrature]

1.462

14877

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

[_quadrature]

0.908

14878

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

[_quadrature]

0.910

14879

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

[_quadrature]

1.043

15494

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

[_quadrature]

0.743

15524

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

[_quadrature]

0.675

15525

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

[_quadrature]

0.679

15561

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

[_quadrature]

0.979

15570

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

[_quadrature]

0.800

15571

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

[_quadrature]

0.865

15572

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

[_quadrature]

0.824

15573

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

[_quadrature]

0.918

15574

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

[_quadrature]

0.842

15575

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

[_quadrature]

1.042

15576

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

[_quadrature]

1.091

15577

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

[_quadrature]

1.173

15578

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

[_quadrature]

2.148

15579

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

[_quadrature]

1.225

15608

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

[_quadrature]

0.997

15809

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

[_quadrature]

0.869

15810

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

[_quadrature]

0.891

15827

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

[_quadrature]

0.928

15831

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

[_quadrature]

0.931

15833

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

[_quadrature]

3.073

15939

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

[_quadrature]

0.958

16152

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

[_quadrature]

1.050

16162

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

[_quadrature]

4.280

16163

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

[_quadrature]

0.755

16164

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

[_quadrature]

1.131

16165

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

[_quadrature]

1.253

16166

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

[_quadrature]

1.112

16167

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

[_quadrature]

0.868

16168

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

[_quadrature]

1.149

16169

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

[_quadrature]

1.046

16170

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

[_quadrature]

0.865

16174

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

[_quadrature]

1.292

16175

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

[_quadrature]

2.012

16176

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

[_quadrature]

1.244

16177

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

[_quadrature]

1.794

16178

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

[_quadrature]

3.135

16179

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

[_quadrature]

1.333

16181

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

[_quadrature]

0.726

16182

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

[_quadrature]

1.019

16183

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

[_quadrature]

0.993

16184

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

[_quadrature]

0.759

16185

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

[_quadrature]

1.558

16186

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

[_quadrature]

1.503

16187

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

[_quadrature]

1.500

16188

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

[_quadrature]

1.062

16189

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

[_quadrature]

1.012

16190

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

[_quadrature]

0.826

16191

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

[_quadrature]

226.372

16192

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

[_quadrature]

1.301

16193

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

[_quadrature]

1.334

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]

1.023

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]

0.937

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]

0.968

16211

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

[_quadrature]

0.917

16262

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

[_quadrature]

0.788

16336

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

[_quadrature]

1.139

16347

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

[_quadrature]

1.053

16352

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

[_quadrature]

1.524

16363

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

[_quadrature]

1.083

16373

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

[_quadrature]

0.833

16961

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

[_quadrature]

0.435

16980

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

[_quadrature]

0.805

16981

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

[_quadrature]

0.711

16982

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

[_quadrature]

0.465

16983

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

[_quadrature]

0.512

16984

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

[_quadrature]

0.432

16985

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

[_quadrature]

0.444

16986

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

[_quadrature]

0.543

16987

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

[_quadrature]

0.578

16988

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

[_quadrature]

0.559

16989

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

[_quadrature]

0.678

16990

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

[_quadrature]

0.484

16991

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

[_quadrature]

1.106

16992

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

[_quadrature]

0.986

17001

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

[_quadrature]

0.583

17002

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

[_quadrature]

0.726

17003

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

[_quadrature]

0.707

17004

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

[_quadrature]

0.562

17011

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

[_quadrature]

0.691

17025

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

[_quadrature]

0.408

17026

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

[_quadrature]

0.615

17027

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

[_quadrature]

0.520

17028

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

[_quadrature]

0.607

17032

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

[_quadrature]

0.615

17033

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

[_quadrature]

0.672

17044

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

[_quadrature]

0.628

17107

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

[_quadrature]

3.756

17108

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

[_quadrature]

0.622

17110

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

[_quadrature]

0.673

17116

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

[_quadrature]

1.128

17117

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

[_quadrature]

0.608

17206

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

[_quadrature]

0.803

17851

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

[_quadrature]

0.387

17863

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

[_quadrature]

0.388

17867

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

[_quadrature]

0.785

17868

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

[_quadrature]

0.613

17895

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

[_quadrature]

0.958

17896

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

[_quadrature]

0.568

17897

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

[_quadrature]

0.381

17898

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

[_quadrature]

0.655

17899

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

[_quadrature]

0.610

17900

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

[_quadrature]

0.310

17901

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

[_quadrature]

0.342

18001

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

[_quadrature]

5.862

18008

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

[_quadrature]

0.411

18049

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

[_quadrature]

0.743

18625

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

[_quadrature]

0.845

19063

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

[_quadrature]

1.576

19064

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

[_quadrature]

1.708

19227

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

[_quadrature]

1.914

19241

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

[_quadrature]

0.645

19242

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

[_quadrature]

0.931

19243

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

[_quadrature]

0.609

19244

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

[_quadrature]

0.567

19245

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

[_quadrature]

0.691

19246

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

[_quadrature]

0.675

19247

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

[_quadrature]

0.906

19248

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

[_quadrature]

0.767

19254

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

[_quadrature]

1.110

19259

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

[_quadrature]

0.790

19260

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

[_quadrature]

0.878

19261

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

[_quadrature]

0.860

19262

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

[_quadrature]

0.931

19263

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

[_quadrature]

0.905

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]

1.126

19266

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

[_quadrature]

0.853

19269

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

[_quadrature]

1.069

19659

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

[_quadrature]

0.901

19660

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

[_quadrature]

0.569

19661

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

[_quadrature]

0.736

19662

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

[_quadrature]

0.839

19663

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

[_quadrature]

0.743

19664

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

[_quadrature]

1.839

19732

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

[_quadrature]

0.573

19737

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

[_quadrature]

0.576

19744

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

[_quadrature]

1.112

20007

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

[_quadrature]

2.691

20023

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

[_quadrature]

4.865

20032

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

[_quadrature]

4.681

20385

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

[_quadrature]

2.175

20425

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

[_quadrature]

3.056

20456

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

[_quadrature]

5.095

20457

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

[_quadrature]

27.116

20462

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

[_quadrature]

5.213

20720

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

[_quadrature]

2.792

20737

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

[_quadrature]

5.432

20738

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

[_quadrature]

1.208

21339

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

[_quadrature]

5.852

21381

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

[_quadrature]

2.454

21473

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

[_quadrature]

21.845

21800

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

[_quadrature]

0.885

21974

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

[_quadrature]

2.695

21999

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

[_quadrature]

1.277

22072

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

[_quadrature]

0.717

22304

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

[_quadrature]

1.338

22305

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

[_quadrature]

1.313

22307

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

[_quadrature]

3.784

22309

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

[_quadrature]

2.464

22351

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

[_quadrature]

3.836

22419

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

[_quadrature]

1.315

22513

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

[_quadrature]

0.872

23055

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

[_quadrature]

1.729

23061

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

[_quadrature]

1.518

23062

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

[_quadrature]

1.964

23063

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

[_quadrature]

6.730

23258

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

[_quadrature]

0.727

23828

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

[_quadrature]

3.109

23829

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

[_quadrature]

0.923

23830

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

[_quadrature]

0.977

23831

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

[_quadrature]

0.881

23832

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

[_quadrature]

1.645

23833

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

[_quadrature]

1.516

23834

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

[_quadrature]

1.034

23839

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

[_quadrature]

1.013

24139

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

[_quadrature]

3.296

24140

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

[_quadrature]

1.997

24141

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

[_quadrature]

2.308

24259

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

[_quadrature]

0.776

24922

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

[_quadrature]

0.935

24923

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

[_quadrature]

0.934

24924

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

[_quadrature]

0.967

24925

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

[_quadrature]

0.973

24932

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

[_quadrature]

1.491

24933

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

[_quadrature]

1.514

24935

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

[_quadrature]

8.027

25041

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

[_quadrature]

1.994

25403

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

[_quadrature]

10.341

25413

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

[_quadrature]

9.727

25417

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

[_quadrature]

5.895

25422

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

[_quadrature]

4.826

25442

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

[_quadrature]

1.135

25647

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

[_quadrature]

2.052

25783

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

[_quadrature]

86.819

25784

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

[_quadrature]

5.136

25805

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

[_quadrature]

3.122

25815

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

[_quadrature]

1.159

25816

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

[_quadrature]

1.185

25817

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

[_quadrature]

2.346

25831

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

[_quadrature]

5.194

25834

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

[_quadrature]

9.944

26130

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

[_quadrature]

83.802

26156

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

[_quadrature]

11.908

26157

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

[_quadrature]

88.930

26158

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

[_quadrature]

3.449

26159

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

[_quadrature]

1.947

26184

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

[_quadrature]

0.973

26196

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

[_quadrature]

0.989

26241

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

[_quadrature]

7.983

26242

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

[_quadrature]

4.171

26243

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

[_quadrature]

3.575

26244

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

[_quadrature]

10.467

26245

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

[_quadrature]

4.242

26246

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

[_quadrature]

2.369

26247

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

[_quadrature]

1.974

26354

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

[_quadrature]

88.978

26364

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

[_quadrature]

1.494

26389

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

[_quadrature]

1.310

26754

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

[_quadrature]

2.063

26923

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

[_quadrature]

9.937

26924

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

[_quadrature]

1.396

27378

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

[_quadrature]

73.030

27379

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

[_quadrature]

19.090

27465

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

[_quadrature]

27.718