2.3.223 Problems 22201 to 22300

Table 2.989: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22201

23057

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

9.691

22202

5353

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

9.692

22203

4783

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

9.694

22204

5755

\begin{align*} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime }&=0 \\ \end{align*}

9.695

22205

25833

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

9.699

22206

20575

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

9.700

22207

23955

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

9.702

22208

4821

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

9.704

22209

5830

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

9.708

22210

14219

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

9.708

22211

16244

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

9.723

22212

5286

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

9.724

22213

733

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

9.728

22214

8709

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

9.728

22215

18626

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

9.732

22216

19383

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

9.735

22217

5894

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

9.747

22218

6839

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

9.749

22219

11340

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

9.750

22220

13352

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

9.757

22221

4793

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

9.758

22222

20315

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

9.758

22223

17939

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

9.761

22224

13248

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

9.763

22225

14251

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

9.764

22226

26225

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

9.766

22227

12048

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

9.770

22228

13459

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

9.771

22229

13649

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

9.772

22230

7471

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

9.780

22231

18596

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

9.785

22232

21386

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

9.789

22233

14198

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

9.793

22234

13870

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

9.794

22235

3038

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

9.797

22236

5266

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

9.813

22237

5459

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

9.816

22238

5428

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

9.817

22239

6842

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

9.821

22240

4782

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

9.823

22241

4895

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

9.825

22242

20245

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

9.828

22243

11371

\begin{align*} y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}}&=0 \\ \end{align*}

9.833

22244

23953

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

9.836

22245

19672

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

9.841

22246

7513

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

9.845

22247

4898

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

9.849

22248

11877

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

9.860

22249

13456

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

9.863

22250

13322

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

9.870

22251

4675

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

9.877

22252

6979

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

9.877

22253

22985

\begin{align*} y^{\prime }-\frac {6 y}{x}&=7 x \\ y \left (1\right ) &= 0 \\ \end{align*}

9.883

22254

5851

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

9.885

22255

4899

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

9.888

22256

5175

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

9.890

22257

6801

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

9.894

22258

24371

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

9.894

22259

5610

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

9.900

22260

23856

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

9.905

22261

6311

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

9.910

22262

4838

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

9.912

22263

17927

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

9.913

22264

11487

\begin{align*} x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\ \end{align*}

9.915

22265

12166

\begin{align*} y^{\prime }&=\frac {2 x^{2}-4 x^{3} y+1+y^{2} x^{4}+x^{6} y^{3}-3 x^{5} y^{2}+3 x^{4} y-x^{3}}{x^{4}} \\ \end{align*}

9.926

22266

23946

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

9.927

22267

19943

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

9.930

22268

20025

\begin{align*} a {y^{\prime }}^{3}&=27 y \\ \end{align*}

9.934

22269

22521

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

9.940

22270

7145

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

9.943

22271

14508

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \\ y \left (0\right ) &= 6 \\ \end{align*}

9.947

22272

22512

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

9.951

22273

14233

\begin{align*} x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}

9.952

22274

14530

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

9.960

22275

5911

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

9.962

22276

21930

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

9.968

22277

20110

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

9.977

22278

11951

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

9.980

22279

23898

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

9.986

22280

5156

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

9.988

22281

22974

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

9.993

22282

13794

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

9.997

22283

4860

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

10.000

22284

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*}

10.001

22285

11966

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

10.003

22286

606

\begin{align*} x^{\prime }&=2 x-3 y \\ y^{\prime }&=x+y+2 z \\ z^{\prime }&=5 y-7 z \\ \end{align*}

10.017

22287

13438

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

10.019

22288

4222

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

10.020

22289

9165

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

10.021

22290

19990

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

10.021

22291

18609

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

10.023

22292

13461

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

10.024

22293

15841

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

10.028

22294

17241

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

10.030

22295

12139

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

10.031

22296

6811

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

10.036

22297

23857

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

10.046

22298

25839

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

10.051

22299

24193

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

10.054

22300

4840

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

10.055