2.4.21 first order ode quadrature

Table 2.1091: first order ode quadrature [363]

#

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]

0.349

2

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

[_quadrature]

1.311

3

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

[_quadrature]

0.566

4

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

[_quadrature]

0.395

5

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

[_quadrature]

0.280

6

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

[_quadrature]

2.464

7

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

[_quadrature]

0.251

8

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

[_quadrature]

0.357

9

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

[_quadrature]

0.264

10

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

[_quadrature]

0.253

651

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

[_quadrature]

0.415

652

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

[_quadrature]

0.421

653

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

[_quadrature]

0.537

654

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

[_quadrature]

0.382

655

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

[_quadrature]

0.230

656

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

[_quadrature]

2.647

657

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

[_quadrature]

0.207

658

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

[_quadrature]

0.266

659

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

[_quadrature]

0.253

660

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

[_quadrature]

1.257

1524

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

[_quadrature]

0.220

1525

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

[_quadrature]

0.174

1526

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

[_quadrature]

0.171

1527

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

[_quadrature]

0.264

1528

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

[_quadrature]

0.299

1529

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

[_quadrature]

1.551

2851

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

[_quadrature]

0.289

3402

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

[_quadrature]

0.685

3403

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

[_quadrature]

0.332

3404

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

[_quadrature]

0.280

3405

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

[_quadrature]

0.329

3406

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

[_quadrature]

0.296

3407

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

[_quadrature]

0.285

3415

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

[_quadrature]

0.307

3416

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

[_quadrature]

0.441

3417

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

[_quadrature]

0.316

3418

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

[_quadrature]

0.308

3419

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

[_quadrature]

0.295

3420

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

[_quadrature]

0.313

3421

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

[_quadrature]

0.299

3422

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

[_quadrature]

0.349

3423

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

[_quadrature]

0.358

3427

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

[_quadrature]

0.447

3428

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

[_quadrature]

0.489

3429

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

[_quadrature]

0.448

3542

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

[_quadrature]

0.171

3581

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

[_quadrature]

0.174

3582

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

[_quadrature]

0.287

3585

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

[_quadrature]

0.293

4090

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

[_quadrature]

0.188

4091

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

[_quadrature]

0.184

4105

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

[_quadrature]

0.369

4107

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

[_quadrature]

0.263

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]

0.506

4386

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

[_quadrature]

170.114

4438

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

[_quadrature]

1.449

4607

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

[_quadrature]

0.193

4749

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

[_quadrature]

0.435

4750

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

[_quadrature]

0.261

4841

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

[_quadrature]

0.240

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]

0.378

5399

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

[_quadrature]

0.937

5411

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

[_quadrature]

0.973

5448

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

[_quadrature]

1.300

5487

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

[_quadrature]

1.339

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]

0.769

5537

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

[_quadrature]

0.806

5621

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

[_quadrature]

3.151

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]

0.945

5685

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

[_quadrature]

5.980

5693

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

[_quadrature]

0.213

5694

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

[_quadrature]

0.214

5698

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

[_quadrature]

0.711

5700

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

[_quadrature]

2.347

6881

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

[_quadrature]

6.517

7406

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

[_quadrature]

1.402

7695

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

[_quadrature]

0.306

7699

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

[_quadrature]

0.369

7894

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

[_quadrature]

0.451

8201

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

[_quadrature]

0.174

8203

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

[_quadrature]

1.924

8257

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

[_quadrature]

0.428

8258

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

[_quadrature]

0.376

8305

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

[_quadrature]

1.882

8306

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

[_quadrature]

2.098

8338

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

[_quadrature]

0.274

8339

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

[_quadrature]

0.199

8340

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

[_quadrature]

0.266

8396

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

[_quadrature]

0.330

8681

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

[_quadrature]

0.250

8855

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

[_quadrature]

0.224

9048

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

[_quadrature]

0.293

9062

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

[_quadrature]

0.202

9063

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

[_quadrature]

0.208

9064

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

[_quadrature]

0.244

9065

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

[_quadrature]

0.238

9066

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

[_quadrature]

0.240

9067

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

[_quadrature]

0.280

9068

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

[_quadrature]

0.200

9069

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

[_quadrature]

0.284

9070

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

[_quadrature]

0.351

9071

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

[_quadrature]

0.267

9072

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

[_quadrature]

0.306

9073

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

[_quadrature]

0.359

9074

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

[_quadrature]

0.335

9075

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

[_quadrature]

0.368

9076

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

[_quadrature]

0.402

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]

0.503

9992

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

[_quadrature]

0.234

9993

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

[_quadrature]

0.346

9995

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

[_quadrature]

0.315

9996

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

[_quadrature]

0.347

10001

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

[_quadrature]

0.386

10011

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

[_quadrature]

0.177

10013

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

[_quadrature]

0.175

10014

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

[_quadrature]

0.166

10259

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

[_quadrature]

0.209

10260

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

[_quadrature]

0.398

10261

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

[_quadrature]

0.296

10262

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

[_quadrature]

0.385

10263

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

[_quadrature]

0.273

10270

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

[_quadrature]

0.224

10271

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

[_quadrature]

0.462

10272

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

[_quadrature]

0.296

10289

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

[_quadrature]

0.235

10290

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

[_quadrature]

0.236

10291

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

[_quadrature]

0.246

10292

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

[_quadrature]

0.238

10293

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

[_quadrature]

0.262

10294

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

[_quadrature]

0.264

10295

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

[_quadrature]

0.302

10296

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

[_quadrature]

0.253

10297

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

[_quadrature]

0.237

10302

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

[_quadrature]

0.272

10303

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

[_quadrature]

0.270

10305

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

[_quadrature]

0.316

10306

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

[_quadrature]

0.451

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]

1.043

11389

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

[_quadrature]

0.429

11673

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

[_quadrature]

8.846

11723

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

[_quadrature]

0.653

11746

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

[_quadrature]

1.693

11809

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

[_quadrature]

5.957

11852

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

[_quadrature]

0.386

11853

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

[_quadrature]

0.380

11856

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

[_quadrature]

1.422

13201

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

[_quadrature]

0.213

14203

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

[_quadrature]

0.366

14204

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

[_quadrature]

0.339

14206

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

[_quadrature]

0.214

14207

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

[_quadrature]

0.210

14208

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

[_quadrature]

0.266

14209

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

[_quadrature]

0.378

14871

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

[_quadrature]

0.271

14872

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

[_quadrature]

0.238

14873

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

[_quadrature]

0.311

14874

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

[_quadrature]

0.266

14875

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

[_quadrature]

0.332

14876

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

[_quadrature]

0.466

14877

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

[_quadrature]

0.368

14878

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

[_quadrature]

0.403

14879

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

[_quadrature]

0.421

15494

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

[_quadrature]

0.276

15524

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

[_quadrature]

0.226

15525

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

[_quadrature]

0.236

15561

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

[_quadrature]

0.453

15570

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

[_quadrature]

0.338

15571

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

[_quadrature]

1.371

15572

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

[_quadrature]

0.377

15573

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

[_quadrature]

0.394

15574

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

[_quadrature]

0.365

15575

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

[_quadrature]

0.322

15576

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

[_quadrature]

0.434

15577

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

[_quadrature]

0.381

15578

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

[_quadrature]

0.533

15579

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

[_quadrature]

0.378

15608

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

[_quadrature]

0.269

15809

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

[_quadrature]

0.253

15810

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

[_quadrature]

0.247

15827

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

[_quadrature]

0.279

15831

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

[_quadrature]

0.257

15833

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

[_quadrature]

0.581

15939

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

[_quadrature]

0.293

16152

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

[_quadrature]

0.207

16155

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

[_quadrature]

0.569

16162

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

[_quadrature]

0.276

16163

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

[_quadrature]

0.217

16164

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

[_quadrature]

0.233

16165

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

[_quadrature]

0.245

16166

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

[_quadrature]

0.207

16167

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

[_quadrature]

0.205

16168

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

[_quadrature]

0.247

16169

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

[_quadrature]

0.267

16170

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

[_quadrature]

0.187

16174

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

[_quadrature]

0.335

16175

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

[_quadrature]

0.373

16176

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

[_quadrature]

0.303

16177

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

[_quadrature]

0.346

16178

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

[_quadrature]

0.707

16179

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

[_quadrature]

0.303

16181

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

[_quadrature]

0.207

16182

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

[_quadrature]

0.297

16183

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

[_quadrature]

0.283

16184

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

[_quadrature]

0.214

16185

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

[_quadrature]

0.316

16186

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

[_quadrature]

0.317

16187

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

[_quadrature]

0.306

16188

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

[_quadrature]

0.290

16189

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

[_quadrature]

0.322

16190

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

[_quadrature]

0.267

16191

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

[_quadrature]

0.320

16192

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

[_quadrature]

0.375

16193

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

[_quadrature]

0.369

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]

0.183

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]

0.181

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]

0.185

16211

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

[_quadrature]

0.214

16262

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

[_quadrature]

0.202

16336

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

[_quadrature]

0.260

16347

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

[_quadrature]

0.268

16352

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

[_quadrature]

0.313

16363

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

[_quadrature]

0.278

16373

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

[_quadrature]

0.230

16961

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

[_quadrature]

0.213

16980

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

[_quadrature]

0.264

16981

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

[_quadrature]

0.230

16982

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

[_quadrature]

0.288

16983

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

[_quadrature]

0.267

16984

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

[_quadrature]

0.247

16985

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

[_quadrature]

0.216

16986

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

[_quadrature]

0.253

16987

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

[_quadrature]

0.289

16988

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

[_quadrature]

0.243

16989

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

[_quadrature]

0.259

16990

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

[_quadrature]

0.311

16991

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

[_quadrature]

0.299

16992

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

[_quadrature]

0.356

17001

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

[_quadrature]

0.315

17002

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

[_quadrature]

0.403

17003

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

[_quadrature]

0.467

17004

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

[_quadrature]

0.358

17011

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

[_quadrature]

0.543

17025

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

[_quadrature]

0.227

17026

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

[_quadrature]

0.246

17027

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

[_quadrature]

0.253

17028

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

[_quadrature]

0.283

17032

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

[_quadrature]

0.374

17033

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

[_quadrature]

0.408

17044

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

[_quadrature]

0.306

17107

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

[_quadrature]

2.887

17108

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

[_quadrature]

0.362

17110

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

[_quadrature]

0.400

17116

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

[_quadrature]

0.423

17117

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

[_quadrature]

0.326

17206

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

[_quadrature]

0.358

17851

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

[_quadrature]

0.266

17863

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

[_quadrature]

0.270

17867

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

[_quadrature]

0.575

17868

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

[_quadrature]

0.361

17895

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

[_quadrature]

0.632

17896

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

[_quadrature]

0.417

17897

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

[_quadrature]

0.329

17898

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

[_quadrature]

0.441

17899

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

[_quadrature]

0.428

17900

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

[_quadrature]

0.296

17901

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

[_quadrature]

0.226

18001

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

[_quadrature]

1.247

18008

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

[_quadrature]

0.175

18049

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

[_quadrature]

0.257

18625

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

[_quadrature]

0.235

19063

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

[_quadrature]

0.370

19064

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

[_quadrature]

0.270

19113

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

[_quadrature]

33.165

19227

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

[_quadrature]

0.622

19241

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

[_quadrature]

0.527

19242

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

[_quadrature]

0.500

19243

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

[_quadrature]

0.415

19244

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

[_quadrature]

0.388

19245

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

[_quadrature]

0.508

19246

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

[_quadrature]

0.437

19247

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

[_quadrature]

0.681

19248

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

[_quadrature]

0.469

19254

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

[_quadrature]

0.627

19259

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

[_quadrature]

0.700

19260

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

[_quadrature]

0.655

19261

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

[_quadrature]

0.843

19262

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

[_quadrature]

0.736

19263

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

[_quadrature]

0.753

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]

1.159

19266

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

[_quadrature]

0.598

19269

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

[_quadrature]

0.673

19659

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

[_quadrature]

0.614

19660

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

[_quadrature]

0.746

19661

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

[_quadrature]

0.542

19662

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

[_quadrature]

0.648

19663

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

[_quadrature]

0.637

19664

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

[_quadrature]

1.203

19732

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

[_quadrature]

0.650

19737

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

[_quadrature]

0.551

19744

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

[_quadrature]

0.421

20007

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

[_quadrature]

0.249

20023

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

[_quadrature]

0.801

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]

0.680

20385

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

[_quadrature]

0.703

20425

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

[_quadrature]

0.509

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]

1.032

20457

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

[_quadrature]

63.197

20461

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

[_quadrature]

1.104

20462

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

[_quadrature]

0.950

20720

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

[_quadrature]

0.998

20737

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

[_quadrature]

1.407

20738

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

[_quadrature]

0.702

21339

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

[_quadrature]

0.702

21381

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

[_quadrature]

0.532

21473

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

[_quadrature]

13.818

21800

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

[_quadrature]

0.548

21974

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

[_quadrature]

0.288

21999

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

[_quadrature]

0.219

22072

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

[_quadrature]

0.191

22304

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

[_quadrature]

0.277

22305

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

[_quadrature]

0.297

22307

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

[_quadrature]

0.570

22309

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

[_quadrature]

0.534

22351

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

[_quadrature]

0.282

22419

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

[_quadrature]

0.393

22513

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

[_quadrature]

0.156

23055

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

[_quadrature]

0.280

23061

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

[_quadrature]

0.304

23062

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

[_quadrature]

0.260

23063

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

[_quadrature]

1.952

23258

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

[_quadrature]

0.207

23828

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

[_quadrature]

0.280

23829

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

[_quadrature]

0.199

23830

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

[_quadrature]

0.172

23831

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

[_quadrature]

0.181

23832

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

[_quadrature]

0.206

23833

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

[_quadrature]

0.194

23834

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

[_quadrature]

0.205

23839

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

[_quadrature]

0.199

24139

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

[_quadrature]

0.334

24140

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

[_quadrature]

0.295

24141

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

[_quadrature]

0.642

24259

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

[_quadrature]

0.355

24922

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

[_quadrature]

0.161

24923

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

[_quadrature]

0.180

24924

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

[_quadrature]

0.194

24925

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

[_quadrature]

0.174

24932

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

[_quadrature]

0.285

24933

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

[_quadrature]

0.322

24935

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

[_quadrature]

0.279

25041

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

[_quadrature]

0.303

25403

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

[_quadrature]

2.910

25413

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

[_quadrature]

0.544

25417

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

[_quadrature]

0.541

25422

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

[_quadrature]

0.465

25442

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

[_quadrature]

0.408

25647

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

[_quadrature]

0.176

25783

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

[_quadrature]

2.667

25784

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

[_quadrature]

2.760

25805

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

[_quadrature]

0.215

25815

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

[_quadrature]

0.227

25816

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

[_quadrature]

0.202

25817

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

[_quadrature]

0.271