2.3.230 Problems 22901 to 23000

Table 2.1033: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22901

22091

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

8.174

22902

22325

\begin{align*} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\ \end{align*}

8.174

22903

24914

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

8.174

22904

6133

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

8.175

22905

24125

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

8.175

22906

21668

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

Series expansion around \(x=0\).

8.177

22907

22059

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

8.181

22908

20307

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

8.182

22909

12210

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

8.187

22910

9342

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

8.188

22911

24159

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

8.188

22912

21961

\begin{align*} {b^{\prime }}^{7}&=3 p \\ \end{align*}

8.191

22913

10280

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

8.192

22914

25743

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

8.202

22915

8719

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

8.204

22916

21043

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

8.207

22917

17081

\begin{align*} \cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime }&=0 \\ \end{align*}

8.209

22918

24224

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

8.223

22919

26290

\begin{align*} 8 x y^{\prime }-y&=-\frac {1}{y^{3} \sqrt {x +1}} \\ \end{align*}

8.224

22920

22150

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

8.229

22921

8434

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

8.239

22922

12139

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

8.240

22923

14515

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

8.241

22924

7031

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

8.243

22925

15554

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

8.243

22926

5180

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

8.244

22927

10408

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

8.245

22928

22975

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

8.246

22929

22384

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

8.254

22930

6555

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

8.257

22931

20823

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

8.257

22932

22533

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

8.259

22933

5303

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

8.263

22934

10406

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

8.263

22935

14192

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

8.268

22936

24397

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

8.272

22937

18503

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

8.276

22938

23135

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

8.276

22939

17927

\begin{align*} 4 y^{6}+x^{3}&=6 x y^{5} y^{\prime } \\ \end{align*}

8.277

22940

9099

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

8.279

22941

21426

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

8.280

22942

15784

\begin{align*} y^{\prime }&=t y^{{1}/{3}} \\ \end{align*}

8.281

22943

18581

\begin{align*} 9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime }&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}

8.283

22944

4213

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

8.284

22945

5278

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

8.285

22946

12145

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

8.295

22947

15137

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

8.295

22948

25735

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

8.296

22949

17915

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

8.297

22950

19798

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

8.297

22951

13454

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

8.298

22952

19098

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

8.301

22953

1503

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right ) \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

8.302

22954

3642

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

8.302

22955

12571

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

8.311

22956

11944

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

8.319

22957

5536

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

8.329

22958

11942

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

8.330

22959

14228

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

8.334

22960

528

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

8.335

22961

15856

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

8.336

22962

18505

\begin{align*} y^{\prime }&=\frac {2 \cos \left (2 x \right )}{10+2 y} \\ y \left (0\right ) &= -1 \\ \end{align*}

8.336

22963

4879

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

8.341

22964

17205

\begin{align*} {\mathrm e}^{y t}+\frac {t \,{\mathrm e}^{y t} y^{\prime }}{y}&=0 \\ \end{align*}

8.341

22965

5030

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

8.343

22966

14449

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

8.343

22967

25841

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

8.343

22968

22877

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

Series expansion around \(x=0\).

8.344

22969

9010

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

8.346

22970

8274

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

8.349

22971

4791

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

8.353

22972

9124

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

8.355

22973

14498

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

8.355

22974

7874

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

8.356

22975

13902

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

8.356

22976

14418

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

8.360

22977

9021

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

8.361

22978

1159

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

8.362

22979

22432

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

8.362

22980

18485

\begin{align*} y^{\prime }&=\left (1-12 x \right ) y^{2} \\ y \left (0\right ) &= -{\frac {1}{8}} \\ \end{align*}

8.377

22981

6420

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

8.378

22982

21472

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

8.387

22983

25683

\begin{align*} 3 x y^{\prime }+5 y&=10 \\ \end{align*}

8.391

22984

19304

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

8.398

22985

4372

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

8.401

22986

5578

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

8.401

22987

17913

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

8.401

22988

15237

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

8.405

22989

12171

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

8.408

22990

5251

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

8.415

22991

14495

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

8.415

22992

24163

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

8.421

22993

20970

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

8.427

22994

15638

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

8.429

22995

26083

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

8.429

22996

9998

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

8.431

22997

10078

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

8.433

22998

19202

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

8.435

22999

26353

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

8.436

23000

21458

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

8.438