2.3.228 Problems 22701 to 22800

Table 2.987: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22701

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*}

6.937

22702

8408

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

6.940

22703

1615

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

6.944

22704

18609

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

6.944

22705

5128

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

6.949

22706

14479

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

6.952

22707

25662

\begin{align*} y^{\prime }&=25+y^{2} \\ \end{align*}

6.954

22708

17965

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

6.957

22709

11652

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

6.960

22710

17917

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

6.965

22711

5332

\begin{align*} f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n}&=0 \\ \end{align*}

6.971

22712

12272

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

6.974

22713

11976

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

6.986

22714

7401

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

6.987

22715

6859

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

6.991

22716

19963

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

6.992

22717

24229

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

6.993

22718

21364

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

6.994

22719

24349

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

6.994

22720

2904

\begin{align*} 6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \\ y \left (-1\right ) &= 1 \\ \end{align*}

6.996

22721

4942

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

6.996

22722

5161

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

6.998

22723

20449

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

6.999

22724

19301

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

7.001

22725

12063

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

7.002

22726

21260

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

7.002

22727

4747

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

7.009

22728

7147

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

7.010

22729

11888

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

7.010

22730

22385

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

7.012

22731

11542

\begin{align*} \left (2 y x +4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y&=0 \\ \end{align*}

7.014

22732

16315

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

7.015

22733

19750

\begin{align*} \theta ^{\prime \prime }-p^{2} \theta &=0 \\ \end{align*}

7.025

22734

11958

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

7.027

22735

14468

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

7.029

22736

4931

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

7.030

22737

11903

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

7.030

22738

13318

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

7.033

22739

15019

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

7.037

22740

21078

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

7.038

22741

22403

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

7.041

22742

19099

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

7.042

22743

4816

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

7.047

22744

2956

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

7.056

22745

2876

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

7.059

22746

17153

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

7.060

22747

16979

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

7.061

22748

21403

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

7.061

22749

21064

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

7.062

22750

4831

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

7.065

22751

23854

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

7.068

22752

4319

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

7.070

22753

4853

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

7.075

22754

19312

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

7.075

22755

10323

\begin{align*} y^{\prime }&=\left (a +b x +c y\right )^{6} \\ \end{align*}

7.083

22756

8699

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

7.084

22757

17297

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

7.084

22758

20255

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

7.087

22759

20959

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

7.087

22760

24391

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

7.087

22761

11939

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

7.090

22762

1709

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

7.093

22763

17203

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

7.093

22764

7558

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

7.095

22765

11573

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

7.095

22766

2910

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

7.098

22767

7923

\begin{align*} \left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }&=2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \\ \end{align*}

7.099

22768

24405

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

7.099

22769

24396

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

7.102

22770

6983

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

7.103

22771

4748

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

7.111

22772

11702

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

7.119

22773

10312

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

7.121

22774

11655

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

7.121

22775

8752

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

7.122

22776

24202

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

7.124

22777

11590

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

7.127

22778

12690

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

7.138

22779

24224

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

7.139

22780

20259

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

7.146

22781

13463

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

7.147

22782

5076

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

7.148

22783

6021

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

7.149

22784

14896

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

7.151

22785

17262

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

7.155

22786

8289

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

7.159

22787

13359

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

7.161

22788

7485

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

7.168

22789

21063

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

7.174

22790

6361

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

7.179

22791

8730

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

7.180

22792

1666

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

7.190

22793

24144

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

7.194

22794

4239

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

7.196

22795

6269

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

7.200

22796

9015

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

7.201

22797

12154

\begin{align*} y^{\prime }&=\frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512} \\ \end{align*}

7.204

22798

5053

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

7.210

22799

5321

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

7.211

22800

4779

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

7.213