2.3.240 Problems 23901 to 24000

Table 2.1023: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23901

15834

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

22.142

23902

17212

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

22.175

23903

16341

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

22.180

23904

164

\begin{align*} y^{\prime }&=\frac {2 y-x +7}{4 x -3 y-18} \\ \end{align*}

22.185

23905

2533

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

22.194

23906

7390

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

22.195

23907

14193

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

22.195

23908

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*}

22.196

23909

15832

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

22.206

23910

14221

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

22.210

23911

24132

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

22.221

23912

1687

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

22.224

23913

17271

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

22.247

23914

22756

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{2}+16 \ln \left (x \right )^{2} \\ \end{align*}

22.251

23915

7714

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

22.263

23916

7873

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

22.292

23917

5708

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

22.294

23918

14232

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

22.300

23919

2919

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

22.307

23920

7250

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

22.338

23921

24355

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

22.348

23922

25505

\begin{align*} y^{\prime }&=\frac {-3 t^{2}-2 y^{2}}{4 t y+6 y^{2}} \\ \end{align*}

22.368

23923

9153

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

22.382

23924

7544

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

22.395

23925

19967

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

22.401

23926

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*}

22.442

23927

2926

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

22.455

23928

6901

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

22.456

23929

24398

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

22.458

23930

24399

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

22.465

23931

7808

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

22.493

23932

7870

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

22.516

23933

1608

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

22.558

23934

25051

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

22.570

23935

4718

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

22.571

23936

14036

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

22.574

23937

26174

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

22.597

23938

12239

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

22.615

23939

9151

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

22.628

23940

18499

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

22.634

23941

7551

\begin{align*} y^{\prime }&=\frac {x -y-1}{x +y+5} \\ \end{align*}

22.640

23942

18535

\begin{align*} y \cos \left (t \right )+\sin \left (t \right ) y^{\prime }&={\mathrm e}^{t} \\ y \left (1\right ) &= a \\ \end{align*}

22.653

23943

12168

\begin{align*} y^{\prime }&=\frac {6 x^{2} y-2 x +1-5 x^{3} y^{2}-2 y x +y^{3} x^{4}}{x^{2} \left (x^{2} y-x +1\right )} \\ \end{align*}

22.658

23944

14357

\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x&=1-\operatorname {Heaviside}\left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

22.685

23945

24003

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

22.685

23946

12935

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

22.712

23947

8752

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

22.713

23948

11513

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

22.751

23949

6998

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

22.775

23950

14437

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

22.776

23951

5309

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

22.793

23952

4247

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

22.800

23953

11658

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

22.804

23954

4890

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

22.819

23955

5228

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

22.838

23956

25054

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

22.843

23957

13563

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

22.851

23958

13623

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

22.855

23959

9149

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

22.857

23960

2503

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

22.865

23961

19950

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

22.873

23962

5422

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

22.911

23963

14883

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

22.924

23964

20153

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

22.926

23965

25506

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

22.945

23966

21074

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

22.949

23967

22019

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

22.956

23968

8726

\begin{align*} y^{\prime }&=\frac {x +3 y-5}{x -y-1} \\ \end{align*}

22.970

23969

3556

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

22.982

23970

5068

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

22.990

23971

22536

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

22.993

23972

13624

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

23.011

23973

9156

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

23.015

23974

21389

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

23.051

23975

14084

\begin{align*} 8 \left (1+y^{\prime }\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \\ \end{align*}

23.056

23976

22025

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

23.081

23977

11556

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

23.102

23978

4078

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

23.108

23979

25183

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

23.115

23980

11794

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

23.120

23981

1752

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\left (6 x -8\right ) y&=0 \\ \end{align*}

23.131

23982

25744

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

23.140

23983

140

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

23.184

23984

2685

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -2 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

23.185

23985

12129

\begin{align*} y^{\prime }&=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \\ \end{align*}

23.191

23986

15649

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

23.195

23987

25188

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

23.202

23988

23869

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

23.219

23989

4419

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

23.225

23990

23859

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

23.229

23991

14467

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

23.237

23992

6400

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

23.257

23993

14450

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

23.260

23994

7867

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

23.291

23995

21428

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

23.298

23996

13714

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

23.318

23997

12125

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

23.325

23998

17262

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

23.325

23999

7251

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

23.337

24000

14714

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

23.355