2.3.223 Problems 22201 to 22300

Table 2.1019: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22201

12247

\begin{align*} y^{\prime }&=-\frac {x \left (-513-432 x -576 x^{5}+720 x^{3} y-1134 x^{2}-456 x^{6}-756 x^{3}-864 x^{4}-378 y-216 y^{3}-288 y x^{8}-540 y^{2}-1296 x^{2} y^{2}+1008 x^{5} y-144 x^{7}-594 x^{2} y-216 x^{6} y^{2}-972 y^{2} x^{4}+288 x^{7} y+432 y^{2} x^{7}-216 x^{4} y-648 x^{2} y^{3}+432 x^{3} y^{2}-288 x^{6} y+864 x^{5} y^{2}-648 x^{4} y^{3}-96 x^{8}-216 x^{6} y^{3}+64 x^{9}\right )}{216 \left (x^{2}+1\right )^{4}} \\ \end{align*}

6.805

22202

6215

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

6.808

22203

4422

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

6.810

22204

11849

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

6.812

22205

17259

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

6.812

22206

12009

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

6.813

22207

14198

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

6.815

22208

16331

\begin{align*} 6+12 x^{2} y^{2}+\left (7 x^{3} y+\frac {x}{y}\right ) y^{\prime }&=0 \\ \end{align*}

6.815

22209

22050

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

6.817

22210

26391

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

6.818

22211

4795

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

6.819

22212

26335

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

6.819

22213

12035

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

6.821

22214

20233

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

6.821

22215

9972

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

6.827

22216

15531

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

6.827

22217

12374

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

6.828

22218

13718

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

6.832

22219

15152

\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cot \left (x \right )&=0 \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= 0 \\ \end{align*}

6.833

22220

13455

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

6.838

22221

15607

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

6.840

22222

22445

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

6.842

22223

17956

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

6.844

22224

22007

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

6.846

22225

13776

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

6.848

22226

22900

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

6.848

22227

15376

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

6.850

22228

1190

\begin{align*} y^{\prime }&=-b \sqrt {y}+a y \\ \end{align*}

6.856

22229

13246

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

6.856

22230

15747

\(\left [\begin {array}{ccccc} 1 & 3 & 5 & 2 & 4 \\ 5 & 2 & 4 & 1 & 3 \\ 4 & 1 & 3 & 5 & 2 \\ 3 & 5 & 2 & 4 & 1 \\ 2 & 4 & 1 & 3 & 5 \end {array}\right ]\)

N/A

N/A

N/A

6.856

22231

12704

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

6.873

22232

19413

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

6.876

22233

4195

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

6.877

22234

27507

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

6.877

22235

5473

\begin{align*} {y^{\prime }}^{2} x -3 y y^{\prime }+9 x^{2}&=0 \\ \end{align*}

6.879

22236

22507

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

6.879

22237

9929

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

Series expansion around \(x=0\).

6.881

22238

20287

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

6.883

22239

12373

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

6.884

22240

1734

\begin{align*} 12 y x +6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

6.888

22241

11929

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

6.888

22242

14492

\begin{align*} \cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4}&=0 \\ \end{align*}

6.888

22243

15253

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

6.888

22244

5668

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

6.891

22245

22803

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

6.897

22246

9139

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

6.898

22247

22326

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

6.898

22248

4732

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

6.901

22249

22443

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

6.901

22250

7933

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

6.902

22251

9782

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

6.903

22252

27462

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

6.907

22253

5636

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

6.911

22254

7158

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

6.915

22255

21538

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

6.917

22256

5066

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

6.920

22257

12256

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

6.920

22258

5371

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

6.922

22259

4675

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

6.923

22260

15343

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

6.925

22261

22003

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

6.925

22262

23222

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

6.926

22263

18925

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & 10\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

6.927

22264

19423

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

6.928

22265

5757

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

6.930

22266

13491

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

6.931

22267

22544

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

6.931

22268

6202

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

6.932

22269

13452

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

6.932

22270

14545

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

6.932

22271

12018

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

6.934

22272

27468

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

6.934

22273

5700

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

6.937

22274

19729

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

6.943

22275

5434

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

6.946

22276

15018

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

6.946

22277

12258

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

6.948

22278

15394

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

6.948

22279

20728

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

6.948

22280

13890

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

6.949

22281

10417

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

6.950

22282

15457

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

6.950

22283

21075

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

6.950

22284

7396

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

6.953

22285

9946

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

Series expansion around \(x=0\).

6.954

22286

14768

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

Series expansion around \(x=0\).

6.956

22287

19799

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

6.959

22288

5601

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

6.960

22289

11999

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

6.960

22290

4224

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

6.964

22291

12972

\begin{align*} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0}&=0 \\ \end{align*}

6.964

22292

15364

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

6.966

22293

7511

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

6.967

22294

25216

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

6.971

22295

13242

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

6.975

22296

22996

\begin{align*} y^{\prime }+4 y&={\mathrm e}^{k x} \\ \end{align*}

6.975

22297

5431

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

6.976

22298

11640

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

6.976

22299

23118

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

6.977

22300

24174

\begin{align*} y^{2}+7 y x +16 x^{2}+x^{2} y^{\prime }&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

6.977