2.3.245 Problems 24401 to 24500

Table 2.1033: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24401

10434

\begin{align*} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \\ \end{align*}

29.847

24402

3479

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

29.856

24403

23210

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

29.889

24404

15650

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

29.901

24405

25044

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

29.905

24406

12539

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

29.909

24407

17231

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

29.916

24408

6191

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

29.920

24409

7548

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

29.924

24410

22293

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

29.933

24411

17813

\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

29.934

24412

2524

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

29.951

24413

23842

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

29.960

24414

19386

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

29.974

24415

24156

\begin{align*} 5 v-u +\left (3 v-7 u \right ) v^{\prime }&=0 \\ \end{align*}

30.001

24416

17086

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

30.030

24417

11648

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

30.040

24418

23542

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \\ \end{align*}

30.045

24419

17954

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

30.066

24420

5260

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

30.070

24421

12403

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

30.104

24422

10017

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

30.129

24423

13384

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

30.144

24424

11846

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

30.151

24425

24354

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

30.152

24426

23182

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

30.153

24427

12374

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

30.183

24428

24363

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

30.213

24429

20115

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

30.225

24430

21361

\begin{align*} x +2 y-4-\left (-5+2 x +y\right ) y^{\prime }&=0 \\ \end{align*}

30.247

24431

24402

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

30.272

24432

5057

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

30.276

24433

7244

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

30.321

24434

22738

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

30.336

24435

14417

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

30.347

24436

2920

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

30.359

24437

22081

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

30.376

24438

11645

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

30.410

24439

13768

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

30.415

24440

11316

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

30.421

24441

12159

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

30.427

24442

23837

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

30.430

24443

9126

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

30.467

24444

13405

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

30.473

24445

7724

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

30.477

24446

5082

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

30.503

24447

17912

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

30.516

24448

9043

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

30.570

24449

4850

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

30.641

24450

23135

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

30.672

24451

13830

\begin{align*} \left (a \,x^{2}+b \right ) y^{\prime \prime }+\left (c \,x^{2}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{2}+d -b \lambda \right ) y&=0 \\ \end{align*}

30.699

24452

2925

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

30.701

24453

16299

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

30.707

24454

23944

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

30.712

24455

2884

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

30.746

24456

13247

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

30.746

24457

2914

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

30.754

24458

11776

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

30.757

24459

19402

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

30.781

24460

13565

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

30.793

24461

20766

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

30.802

24462

23298

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

30.803

24463

13575

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

30.812

24464

5177

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

30.822

24465

13610

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

30.835

24466

11997

\begin{align*} y^{\prime }&=\frac {-x^{2}+x +2+2 x^{3} \sqrt {x^{2}-4 x +4 y}}{2 x +2} \\ \end{align*}

30.839

24467

13769

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

30.850

24468

11399

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

30.865

24469

12382

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

30.866

24470

21160

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

30.873

24471

2879

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

30.916

24472

13892

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

30.920

24473

5233

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

30.967

24474

2873

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

31.016

24475

24829

\begin{align*} 8 y&={y^{\prime }}^{2}+3 x^{2} \\ \end{align*}

31.028

24476

17922

\begin{align*} 2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\ \end{align*}

31.072

24477

1248

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

31.077

24478

2350

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

31.097

24479

13330

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

31.104

24480

5146

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

31.116

24481

2893

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

31.118

24482

17269

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

31.120

24483

5017

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

31.164

24484

22758

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

31.173

24485

15256

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

31.183

24486

2898

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

31.201

24487

4944

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

31.245

24488

23299

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

31.252

24489

13324

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

31.378

24490

15479

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

31.415

24491

7018

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

31.425

24492

22572

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

31.458

24493

5205

\begin{align*} x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\ \end{align*}

31.460

24494

23959

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

31.490

24495

4356

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

31.510

24496

6190

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

31.553

24497

17979

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

31.569

24498

19719

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

31.601

24499

12319

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

31.607

24500

17214

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

31.626