2.3.235 Problems 23401 to 23500

Table 2.1013: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23401

4394

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

15.981

23402

15557

\begin{align*} y^{\prime }&=-\frac {y}{x}+y^{{1}/{4}} \\ \end{align*}

15.985

23403

8253

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

15.993

23404

10406

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

16.007

23405

19935

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

16.012

23406

15880

\begin{align*} w^{\prime }&=3 w^{3}-12 w^{2} \\ \end{align*}

16.022

23407

7930

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

16.032

23408

16291

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

16.035

23409

10068

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

16.061

23410

2519

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

16.082

23411

25663

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

16.093

23412

13909

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

16.100

23413

26165

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

16.112

23414

25718

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

16.118

23415

14018

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

16.138

23416

12040

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

16.158

23417

5081

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

16.160

23418

11370

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

16.164

23419

19906

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

16.169

23420

6899

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

16.179

23421

14514

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

16.180

23422

9456

\begin{align*} i^{\prime \prime }+2 i^{\prime }+3 i&=\left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \\ i \left (0\right ) &= 8 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

16.194

23423

8673

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

16.199

23424

12150

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

16.206

23425

21973

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

16.209

23426

2867

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

16.217

23427

11975

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

16.221

23428

13511

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

16.230

23429

7863

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

16.240

23430

17965

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

16.243

23431

4362

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

16.256

23432

5074

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

16.258

23433

13916

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

16.275

23434

25210

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

16.292

23435

5140

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

16.308

23436

4966

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

16.318

23437

6859

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

16.321

23438

4779

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

16.342

23439

11519

\begin{align*} \left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \\ \end{align*}

16.346

23440

24297

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

16.348

23441

13430

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

16.355

23442

15062

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

16.367

23443

21807

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

16.378

23444

21597

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

16.387

23445

12210

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

16.393

23446

22382

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

16.396

23447

4891

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

16.397

23448

12144

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

16.415

23449

25030

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

16.439

23450

13555

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

16.443

23451

15856

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

16.454

23452

15798

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

16.461

23453

19802

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

16.461

23454

8695

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

16.464

23455

24368

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

16.465

23456

5925

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

16.466

23457

12854

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

16.475

23458

2928

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

16.477

23459

14118

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

16.478

23460

15638

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

16.489

23461

22424

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

16.500

23462

13643

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

16.503

23463

14913

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

16.503

23464

5255

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

16.519

23465

3031

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

16.525

23466

17091

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

16.539

23467

5703

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

16.558

23468

2358

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

16.565

23469

24344

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

16.577

23470

6880

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

16.594

23471

4239

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

16.616

23472

18573

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

16.618

23473

20103

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

16.619

23474

15640

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

16.630

23475

12612

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

16.645

23476

20470

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

16.645

23477

22064

\begin{align*} y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\ \end{align*}

16.677

23478

5142

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

16.684

23479

1707

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

16.698

23480

11516

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

16.698

23481

5125

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

16.707

23482

13646

\begin{align*} y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}-b m \,x^{m -1}-2 a \,b^{3} x^{n +3 m} \\ \end{align*}

16.717

23483

1650

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

16.720

23484

14236

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

16.732

23485

19068

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

16.739

23486

20469

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

16.765

23487

15943

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

16.783

23488

26240

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

16.808

23489

4432

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

16.816

23490

2333

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

16.822

23491

14505

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

16.891

23492

5304

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

16.895

23493

5212

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

16.902

23494

17294

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

16.911

23495

5064

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

16.928

23496

22358

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

16.928

23497

12678

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

16.947

23498

4948

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

16.948

23499

18552

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

16.949

23500

24296

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

16.959