2.3.245 Problems 24401 to 24500

Table 2.1063: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24401

25885

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

13.303

24402

5098

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

13.309

24403

20510

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

13.316

24404

9157

\begin{align*} y^{\prime }&=\frac {x +y+4}{x +y-6} \\ \end{align*}

13.318

24405

5353

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

13.325

24406

8697

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

13.326

24407

25676

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

13.327

24408

25757

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

13.336

24409

17959

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

13.341

24410

13322

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

13.343

24411

4816

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

13.345

24412

4809

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

13.348

24413

14227

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

13.350

24414

16302

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

13.358

24415

23208

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

13.363

24416

15627

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

13.366

24417

21836

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

13.401

24418

14536

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

13.404

24419

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*}

13.405

24420

5608

\begin{align*} {y^{\prime }}^{3}&=a \,x^{n} \\ \end{align*}

13.408

24421

13327

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

13.408

24422

4314

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

13.414

24423

4738

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

13.417

24424

27206

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

13.418

24425

4391

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

13.421

24426

22046

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

13.424

24427

17815

\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

13.428

24428

3647

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

13.434

24429

5832

\begin{align*} \left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

13.437

24430

26059

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

13.437

24431

24356

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

13.438

24432

15139

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

13.443

24433

6963

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

13.448

24434

5088

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

13.451

24435

11566

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

13.456

24436

13311

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

13.459

24437

4706

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

13.466

24438

21992

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

13.472

24439

15038

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

13.478

24440

13411

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

13.485

24441

12598

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

13.493

24442

12273

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

13.498

24443

24150

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

13.502

24444

8026

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

13.503

24445

5100

\begin{align*} \left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y&=0 \\ \end{align*}

13.504

24446

27611

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

13.510

24447

15477

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

13.512

24448

16955

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

13.519

24449

23461

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

13.521

24450

22472

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

13.523

24451

21059

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

13.530

24452

18011

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

13.536

24453

8699

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

13.540

24454

6468

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

13.541

24455

18070

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

13.543

24456

3553

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

13.547

24457

8713

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

13.551

24458

24385

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

13.551

24459

6469

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

13.553

24460

21369

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

13.553

24461

21801

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

13.566

24462

12485

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

13.567

24463

26326

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

13.574

24464

5616

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

13.579

24465

27461

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

13.579

24466

9791

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

13.582

24467

27325

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

13.585

24468

13276

\begin{align*} x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s&=0 \\ \end{align*}

13.587

24469

20248

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

13.603

24470

25745

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

13.616

24471

25469

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

13.635

24472

6589

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

13.648

24473

7860

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

13.648

24474

25824

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

13.648

24475

22446

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

13.652

24476

24181

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

13.652

24477

23220

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

13.653

24478

15235

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

Using Laplace transform method.

13.658

24479

22962

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

13.663

24480

7018

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

13.667

24481

13418

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

13.669

24482

5764

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

13.670

24483

24316

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

13.679

24484

13416

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

13.683

24485

21622

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

13.689

24486

3282

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

13.691

24487

24334

\begin{align*} x +2 y-1-\left (x +2 y-5\right ) y^{\prime }&=0 \\ \end{align*}

13.698

24488

7737

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

13.701

24489

24405

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

13.702

24490

5866

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

13.704

24491

13523

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

13.706

24492

15628

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

13.710

24493

5846

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

13.729

24494

14232

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

13.732

24495

11364

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

13.746

24496

9007

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

13.756

24497

17094

\begin{align*} y^{\prime }&=\frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \\ \end{align*}

13.776

24498

5084

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

13.781

24499

4949

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

13.782

24500

19320

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

13.792