2.3.160 Problems 15901 to 16000

Table 2.863: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15901

22654

\begin{align*} 4 y+y^{\prime \prime }&=0 \\ \end{align*}

2.217

15902

14780

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

2.218

15903

7445

\begin{align*} u^{\prime }&=\alpha \left (1-u\right )-\beta u \\ \end{align*}

2.219

15904

10418

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

2.219

15905

20771

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

2.219

15906

1179

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

2.220

15907

7928

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

2.221

15908

14667

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

2.221

15909

15583

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

2.221

15910

15598

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

2.221

15911

1215

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

2.222

15912

6812

\begin{align*} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=5 {y^{\prime \prime \prime }}^{2} \\ \end{align*}

2.222

15913

12923

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

2.222

15914

18957

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=1-\operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

2.223

15915

20399

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

2.223

15916

3410

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

2.224

15917

8468

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

2.224

15918

8645

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (\pi \right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 2 \,{\mathrm e}^{-\pi }-2 \\ \end{align*}
Using Laplace transform method.

2.224

15919

12925

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

2.224

15920

19285

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

2.224

15921

6428

\begin{align*} y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+{y^{\prime }}^{2} \\ \end{align*}

2.225

15922

8759

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

2.225

15923

12348

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

2.225

15924

16469

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

2.225

15925

25436

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

2.225

15926

25730

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

2.225

15927

694

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

2.226

15928

24921

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

2.226

15929

2385

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

2.227

15930

22350

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

2.227

15931

8470

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

2.228

15932

24687

\begin{align*} y^{\left (6\right )}-y&=x^{10} \\ \end{align*}

2.229

15933

2308

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

2.230

15934

6027

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

2.230

15935

8535

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

2.230

15936

59

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

2.231

15937

8540

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

2.231

15938

24984

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

2.231

15939

24938

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

2.232

15940

25665

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

2.232

15941

14164

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

2.233

15942

20804

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

2.233

15943

25473

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

2.235

15944

1128

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

2.236

15945

3697

\begin{align*} y^{\prime \prime }-36 y&=0 \\ \end{align*}

2.236

15946

15897

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

2.236

15947

18743

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

2.236

15948

20297

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

2.236

15949

1126

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

2.237

15950

19433

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

2.237

15951

4099

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

2.238

15952

8318

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

2.238

15953

8539

\begin{align*} y^{\prime \prime } x +y^{\prime }+\left (x -\frac {4}{x}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.238

15954

7927

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

2.239

15955

6360

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

2.240

15956

9823

\begin{align*} x^{6} {y^{\prime }}^{2}&=8 y^{\prime } x +16 y \\ \end{align*}

2.240

15957

258

\begin{align*} y^{\prime \prime }-4 y&=12 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

2.241

15958

13764

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

2.241

15959

4032

\begin{align*} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.242

15960

12607

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

2.242

15961

22682

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

2.242

15962

26228

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

2.242

15963

727

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

2.243

15964

18519

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

2.243

15965

25223

\begin{align*} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \\ \end{align*}

2.243

15966

15489

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

2.244

15967

24948

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

2.244

15968

20576

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

2.245

15969

1568

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

2.246

15970

11867

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

2.246

15971

14140

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

2.246

15972

21046

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

2.247

15973

205

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

2.248

15974

8862

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

2.250

15975

9345

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

2.250

15976

14755

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

2.250

15977

18029

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

2.250

15978

1149

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

2.251

15979

4058

\begin{align*} y^{\prime \prime } x -y^{\prime } x +y&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.253

15980

9236

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\ \end{align*}

2.253

15981

14149

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

2.253

15982

20017

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

2.253

15983

25829

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

2.253

15984

7920

\begin{align*} i^{\prime }-6 i&=10 \sin \left (2 t \right ) \\ \end{align*}

2.254

15985

15562

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

2.254

15986

21011

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

2.254

15987

21670

\begin{align*} y^{\prime \prime }+p \left (x \right ) y^{\prime }+q \left (x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

2.255

15988

25235

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

2.255

15989

7727

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

2.256

15990

8452

\begin{align*} \left (x +1\right ) y^{\prime }+y&=\ln \left (x \right ) \\ y \left (1\right ) &= 10 \\ \end{align*}

2.256

15991

15327

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

2.257

15992

23244

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

2.257

15993

25439

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

2.257

15994

8432

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

2.258

15995

1141

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

2.259

15996

3026

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

2.259

15997

6473

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

2.259

15998

9629

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

2.259

15999

11898

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

2.259

16000

14360

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

2.259