2.3.256 Problems 25501 to 25600

Table 2.1061: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25501

8360

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

49.737

25502

15631

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

49.748

25503

21360

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

49.819

25504

15594

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

49.886

25505

13907

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

49.899

25506

9661

\begin{align*} x^{\prime }&=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }&=4 x+y+z+2 \,{\mathrm e}^{5 t} \\ z^{\prime }&=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \\ \end{align*}

49.906

25507

13263

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

49.936

25508

6170

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

49.964

25509

7503

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

49.984

25510

25445

\begin{align*} z^{\prime }+4 z&={\mathrm e}^{8 i t} \\ \end{align*}

49.995

25511

3649

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

50.125

25512

2934

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

50.180

25513

6448

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

50.253

25514

5532

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

50.306

25515

13715

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

50.324

25516

6920

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

50.335

25517

7385

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

50.335

25518

16325

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

50.513

25519

13417

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

50.523

25520

12169

\begin{align*} y^{\prime }&=-\frac {\left (-8-8 y^{3}+24 y^{{3}/{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{{9}/{2}}+36 y^{3} {\mathrm e}^{x}-54 \,{\mathrm e}^{2 x} y^{{3}/{2}}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \\ \end{align*}

50.639

25521

25447

\begin{align*} z^{\prime }+4 i z&={\mathrm e}^{8 t} \\ \end{align*}

50.648

25522

5110

\begin{align*} \left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \\ \end{align*}

50.653

25523

20961

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

50.878

25524

18731

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

50.931

25525

12082

\begin{align*} y^{\prime }&=\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \\ \end{align*}

50.935

25526

19819

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=5 x -7 y \\ \end{align*}

50.976

25527

20427

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

51.026

25528

20742

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

51.049

25529

12249

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

51.109

25530

599

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

51.181

25531

4989

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

51.223

25532

5038

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

51.227

25533

13393

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

51.262

25534

13800

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

51.316

25535

17037

\begin{align*} y^{\prime }&=y^{{1}/{5}} \\ y \left (0\right ) &= 0 \\ \end{align*}

51.344

25536

13799

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

51.357

25537

21835

\begin{align*} 4 x +3 y+2+\left (5 x +4 y+1\right ) y^{\prime }&=0 \\ \end{align*}

51.507

25538

5090

\begin{align*} \left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\ \end{align*}

51.634

25539

24358

\begin{align*} x +3 y-4+\left (x +4 y-5\right ) y^{\prime }&=0 \\ \end{align*}

51.690

25540

23902

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

51.753

25541

13797

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

51.779

25542

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*}

51.826

25543

13802

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

51.864

25544

15629

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

51.934

25545

2820

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

51.956

25546

13555

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

51.981

25547

5475

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

51.995

25548

13847

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

52.019

25549

12068

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

52.035

25550

5323

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

52.038

25551

10073

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

52.106

25552

12612

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

52.123

25553

26313

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

52.217

25554

15650

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

52.342

25555

24177

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

52.345

25556

21824

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

52.347

25557

13917

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

52.357

25558

21389

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

52.372

25559

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*}

52.373

25560

12113

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

52.446

25561

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*}

52.504

25562

6889

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

52.505

25563

11905

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

52.557

25564

22447

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

52.636

25565

12596

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

52.664

25566

2943

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

52.673

25567

7713

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

52.712

25568

5232

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

52.717

25569

23257

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

52.802

25570

20129

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

52.882

25571

13505

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

52.898

25572

3323

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

52.917

25573

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*}

52.931

25574

1664

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

53.018

25575

12623

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

53.083

25576

20958

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

53.084

25577

5106

\begin{align*} \left (11-11 x -4 y\right ) y^{\prime }&=62-8 x -25 y \\ \end{align*}

53.137

25578

12993

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

53.158

25579

19818

\begin{align*} \left (5 x -2 y+7\right ) y^{\prime }&=x -3 y+2 \\ \end{align*}

53.171

25580

14865

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

53.254

25581

20601

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

53.283

25582

12094

\begin{align*} y^{\prime }&=\frac {x^{2}}{2}+\sqrt {x^{3}-6 y}+x^{2} \sqrt {x^{3}-6 y}+x^{3} \sqrt {x^{3}-6 y} \\ \end{align*}

53.389

25583

6369

\begin{align*} 2 y^{\prime \prime }&=1+12 y^{2} \\ \end{align*}

53.504

25584

13535

\begin{align*} y y^{\prime }-y&=12 x +\frac {A}{x^{{5}/{2}}} \\ \end{align*}

53.536

25585

12034

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

53.580

25586

14841

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

53.603

25587

13211

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

53.609

25588

5172

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

53.683

25589

18598

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

53.722

25590

7029

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

53.956

25591

12491

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

53.957

25592

21598

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

53.974

25593

6559

\begin{align*} \left (-\left (1-y\right ) \left (-y+a \right )+y \left (1-y\right )+\left (-y+a \right ) y\right ) {y^{\prime }}^{2}+2 \left (1-y\right ) \left (-y+a \right ) y y^{\prime \prime }&=\operatorname {a3} \left (1-y\right )^{2} \left (-y+a \right )^{2}+\operatorname {a1} \left (1-y\right )^{2} y^{2}+\operatorname {a2} \left (-y+a \right )^{2} y^{2}+\operatorname {a0} \left (-y+a \right )^{2} y^{2} \left (1-y^{2}\right ) \\ \end{align*}

54.072

25594

13264

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

54.072

25595

24963

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

54.098

25596

8836

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

54.124

25597

13304

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

54.161

25598

24387

\begin{align*} \left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\ \end{align*}

54.332

25599

4375

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

54.369

25600

4321

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

54.516