2.3.223 Problems 22201 to 22300

Table 2.995: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22201

11957

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

8.759

22202

11655

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

8.765

22203

7467

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

8.766

22204

11598

\begin{align*} \left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2}&=0 \\ \end{align*}

8.771

22205

11987

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

8.773

22206

24997

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

8.773

22207

11486

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

8.774

22208

4785

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

8.778

22209

12137

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {1}{x}-\textit {\_F1} \left (y^{2}-2 x \right )\right ) x}{\sqrt {y^{2}}} \\ \end{align*}

8.780

22210

15616

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

8.780

22211

5325

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

8.789

22212

8801

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

8.797

22213

11730

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

8.797

22214

7524

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

8.800

22215

12381

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

8.804

22216

4705

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

8.805

22217

6845

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

8.805

22218

11913

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

8.810

22219

26202

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

8.812

22220

17923

\begin{align*} 8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\ \end{align*}

8.819

22221

4854

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

8.820

22222

21321

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

8.837

22223

7393

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

8.839

22224

15165

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

8.841

22225

12345

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

8.845

22226

17910

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

8.846

22227

24819

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

8.849

22228

20429

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

8.855

22229

26173

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

8.857

22230

4822

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

8.861

22231

15374

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

8.864

22232

23959

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

8.871

22233

5065

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

8.875

22234

19320

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

8.878

22235

21320

\begin{align*} x^{\prime \prime }+6 x^{5}&=0 \\ x \left (0\right ) &= 0 \\ x \left (b \right ) &= 0 \\ \end{align*}

8.881

22236

12142

\begin{align*} y^{\prime }&=-\frac {\left (-\frac {y \,{\mathrm e}^{\frac {1}{x}}}{x}-\textit {\_F1} \left (y \,{\mathrm e}^{\frac {1}{x}}\right )\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \\ \end{align*}

8.885

22237

108

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

8.886

22238

3551

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

8.886

22239

21194

\begin{align*} x^{\left (5\right )}+x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

8.886

22240

13720

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

8.889

22241

12225

\begin{align*} y^{\prime }&=\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 x^{4} y+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 x^{5} a +12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64} \\ \end{align*}

8.891

22242

13380

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

8.892

22243

4926

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

8.894

22244

12335

\begin{align*} y^{\prime \prime }+a \,x^{-1+q} y^{\prime }+b \,x^{q -2} y&=0 \\ \end{align*}

8.898

22245

11347

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

8.900

22246

12228

\begin{align*} y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 y^{4} x +4 y^{8}+12 y^{7}+33 y^{6}} \\ \end{align*}

8.905

22247

12329

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

8.910

22248

24374

\begin{align*} 4 y^{2}+10 y x -4 y+8+x \left (2 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}

8.912

22249

8253

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

8.914

22250

4211

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

8.920

22251

24125

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

8.922

22252

3464

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

8.923

22253

3295

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

8.927

22254

12220

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

8.933

22255

25676

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

8.935

22256

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*}

8.937

22257

20736

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

8.938

22258

2971

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

8.942

22259

5203

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

8.942

22260

5040

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

8.949

22261

21456

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

8.954

22262

4777

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

8.956

22263

11496

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

8.956

22264

4676

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

8.958

22265

5103

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

8.962

22266

6023

\begin{align*} x^{2} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

8.963

22267

4885

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

8.965

22268

6886

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

8.965

22269

3475

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

8.969

22270

24959

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

8.969

22271

7338

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

8.970

22272

21990

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

8.970

22273

13485

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

8.971

22274

7874

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

8.973

22275

1597

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

8.974

22276

19823

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

8.980

22277

9096

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

8.981

22278

5756

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

8.983

22279

15184

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

8.987

22280

23147

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

8.987

22281

17203

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

8.994

22282

11915

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

9.001

22283

10408

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

9.003

22284

13313

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

9.007

22285

4667

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

9.008

22286

5819

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

9.010

22287

10121

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

9.014

22288

23869

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

9.021

22289

21063

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

9.026

22290

12121

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

9.027

22291

12198

\begin{align*} y^{\prime }&=\frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 y^{4} x +32 y^{6} x^{2}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\ \end{align*}

9.035

22292

18545

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

9.039

22293

144

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

9.042

22294

21988

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

9.043

22295

8268

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

9.051

22296

12466

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

9.051

22297

14713

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

9.053

22298

1351

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

9.054

22299

3043

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

9.057

22300

109

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

9.061