2.3.257 Problems 25601 to 25700

Table 2.1087: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25601

11543

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

20.823

25602

12130

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

20.853

25603

5686

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

20.879

25604

27258

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

20.897

25605

20262

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

20.903

25606

5476

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

20.908

25607

11633

\begin{align*} \left (\frac {\operatorname {e1} \left (a +x \right )}{\left (\left (a +x \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (a +x \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right )&=0 \\ \end{align*}

20.917

25608

15289

\begin{align*} x^{\prime }&=7 x-4 y+10 \,{\mathrm e}^{t} \\ y^{\prime }&=3 x+14 y+6 \,{\mathrm e}^{2 t} \\ \end{align*}

With initial conditions

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

20.925

25609

12122

\begin{align*} y^{\prime }&=\frac {b \,x^{3}+c^{2} \sqrt {a}-2 c b \,x^{2} \sqrt {a}+2 c y^{2} a^{{3}/{2}}+b^{2} x^{4} \sqrt {a}-2 y^{2} a^{{3}/{2}} b \,x^{2}+a^{{5}/{2}} y^{4}}{a \,x^{2} y} \\ \end{align*}

20.948

25610

17271

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

20.958

25611

13262

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

20.970

25612

7148

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

20.973

25613

8159

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

20.973

25614

6000

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

20.991

25615

13442

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

21.000

25616

14555

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

21.023

25617

24061

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

21.026

25618

8157

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

21.031

25619

13314

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

21.042

25620

12248

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

21.075

25621

11591

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

21.105

25622

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*}

21.124

25623

5702

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

21.128

25624

1687

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

21.150

25625

20589

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

21.158

25626

24181

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

21.158

25627

24172

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

21.216

25628

5119

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

21.235

25629

24157

\begin{align*} x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

21.240

25630

12164

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

21.264

25631

6330

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

21.292

25632

11504

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

21.299

25633

24161

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

21.319

25634

5173

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

21.323

25635

17064

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

21.352

25636

7031

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

21.362

25637

17635

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

21.378

25638

23878

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

21.380

25639

15024

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

21.381

25640

24324

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

21.404

25641

9080

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

21.407

25642

15155

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

21.411

25643

13248

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

21.423

25644

5502

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

21.452

25645

20292

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

21.474

25646

16285

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

21.487

25647

3666

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

21.510

25648

17153

\begin{align*} y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \\ \end{align*}

21.536

25649

5263

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

21.559

25650

12463

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

21.565

25651

22580

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

21.571

25652

9167

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

21.574

25653

11679

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

21.608

25654

11673

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

21.610

25655

5993

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

21.654

25656

11832

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

21.682

25657

27162

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=x_{3} \\ x_{3}^{\prime }&=x_{4} \\ x_{4}^{\prime }&=-x_{1}-2 x_{2} \\ \end{align*}

21.700

25658

14010

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

21.704

25659

19373

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

21.704

25660

5062

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

21.707

25661

13329

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

21.713

25662

7218

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

21.715

25663

5994

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

21.746

25664

15834

\begin{align*} \theta ^{\prime }&=\frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \\ \end{align*}

21.753

25665

12236

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

21.757

25666

13436

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

21.774

25667

13332

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

21.818

25668

26869

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

21.828

25669

15821

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

21.874

25670

20442

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

21.875

25671

20103

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

21.877

25672

4415

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

21.892

25673

5063

\begin{align*} \left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \\ \end{align*}

21.894

25674

16962

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

21.898

25675

26915

\begin{align*} y^{\prime }&=\frac {2 y+x +7}{-2 x +y-9} \\ \end{align*}

21.910

25676

13338

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

21.917

25677

23122

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

21.925

25678

20021

\begin{align*} \left (1+y^{\prime }\right )^{3}&=\frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a} \\ \end{align*}

21.951

25679

2498

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

21.955

25680

13465

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

21.956

25681

27233

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

21.966

25682

15832

\begin{align*} \theta ^{\prime }&=\frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \\ \end{align*}

22.003

25683

5262

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

22.006

25684

15356

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

22.015

25685

13494

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

22.030

25686

5781

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

22.043

25687

3654

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

22.074

25688

17215

\begin{align*} 3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\ \end{align*}

22.087

25689

16153

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

22.092

25690

12482

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

22.108

25691

21598

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

22.144

25692

3029

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

22.183

25693

21036

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

22.185

25694

25037

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

22.208

25695

9153

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

22.216

25696

2770

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }&=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t} \\ \end{align*}

22.217

25697

11848

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

22.226

25698

19812

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

22.239

25699

10119

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

22.241

25700

17212

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

22.251