2.3.260 Problems 25901 to 26000

Table 2.1093: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25901

2346

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

29.204

25902

5352

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

29.213

25903

11326

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

29.213

25904

17278

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

29.286

25905

13486

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

29.293

25906

8404

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

29.306

25907

11648

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

29.329

25908

1723

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

29.336

25909

11316

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

29.387

25910

5632

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

29.398

25911

2349

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

29.401

25912

22515

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

29.408

25913

11649

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

29.421

25914

12248

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

29.491

25915

7470

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

29.507

25916

1123

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

29.522

25917

13337

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

29.556

25918

4255

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

29.570

25919

18356

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

29.577

25920

2526

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

29.601

25921

5988

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

29.606

25922

25507

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

29.609

25923

24336

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

29.611

25924

10269

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

29.630

25925

13918

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

29.662

25926

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*}

29.711

25927

3667

\begin{align*} 2 y^{\prime }+y \cot \left (x \right )&=\frac {8 \cos \left (x \right )^{3}}{y} \\ \end{align*}

29.720

25928

17254

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

29.722

25929

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*}

29.751

25930

2524

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

29.798

25931

8731

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

29.802

25932

4276

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

29.806

25933

17253

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

29.837

25934

14444

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

29.840

25935

25029

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

29.851

25936

2995

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

29.940

25937

5082

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

29.954

25938

6191

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

29.987

25939

11512

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

29.993

25940

22992

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

29.998

25941

15131

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

30.003

25942

1754

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

30.010

25943

21820

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

30.010

25944

13405

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

30.016

25945

2880

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

30.026

25946

2669

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

Series expansion around \(t=0\).

30.034

25947

17917

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

30.046

25948

7462

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

30.104

25949

5529

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

30.126

25950

2896

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

30.137

25951

26323

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

30.147

25952

4318

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

30.165

25953

16330

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

30.193

25954

13648

\begin{align*} 9 y^{\prime }&=-x^{m} \left (a \,x^{1-m}+b \right )^{2 \lambda +1} y^{3}-x^{-2 m} \left (9 a +2+9 b m \,x^{m -1}\right ) \left (a \,x^{1-m}+b \right )^{-\lambda -2} \\ \end{align*}

30.228

25955

13238

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

30.229

25956

2348

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

30.233

25957

764

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

30.236

25958

26679

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

30.247

25959

25852

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

30.276

25960

9134

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

30.329

25961

2922

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

30.344

25962

2335

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

30.349

25963

11405

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

30.356

25964

22081

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

30.376

25965

24354

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

30.386

25966

15644

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

30.438

25967

22442

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

30.474

25968

19386

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

30.478

25969

3579

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

30.479

25970

1834

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

30.496

25971

13247

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

30.513

25972

8824

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

30.527

25973

4258

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

30.529

25974

1248

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

30.531

25975

3639

\begin{align*} x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \\ \end{align*}

30.557

25976

20760

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

30.559

25977

5142

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

30.566

25978

27452

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

30.569

25979

11388

\begin{align*} 2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x}&=0 \\ \end{align*}

30.573

25980

2898

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

30.608

25981

18362

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

30.609

25982

3035

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

30.615

25983

16324

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

30.619

25984

14909

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

30.628

25985

5658

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

30.641

25986

6908

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

30.686

25987

4989

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

30.688

25988

13982

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

30.691

25989

11665

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

30.715

25990

13976

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

30.731

25991

14003

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

30.736

25992

11776

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

30.790

25993

5003

\begin{align*} x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\ \end{align*}

30.792

25994

20766

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

30.802

25995

6921

\begin{align*} y+7+\left (2 x +y+3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

30.803

25996

23298

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

30.803

25997

7492

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

30.804

25998

12437

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

30.822

25999

4668

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

30.832

26000

5197

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

30.842