2.3.238 Problems 23701 to 23800

Table 2.1049: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23701

5846

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

9.074

23702

23859

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

9.074

23703

16979

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

9.077

23704

12221

\begin{align*} y^{\prime }&=\frac {-32 y x -72 x^{3}+32 x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}-192 x y^{2}+12 x^{4} y-96 x^{3} y+192 x^{2} y+x^{6}-12 x^{5}+48 x^{4}}{64 y+16 x^{2}-64 x +64} \\ \end{align*}

9.078

23705

24357

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

9.079

23706

12656

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

9.086

23707

11489

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

9.088

23708

20404

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

9.090

23709

26153

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

9.092

23710

5178

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

9.096

23711

12037

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

9.096

23712

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*}

9.099

23713

13810

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

9.099

23714

13035

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

9.101

23715

5099

\begin{align*} \left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y&=0 \\ \end{align*}

9.105

23716

16695

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

9.114

23717

22958

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

9.118

23718

5097

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

9.121

23719

27285

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

9.124

23720

16694

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

9.125

23721

11941

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

9.127

23722

16296

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

9.134

23723

24163

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

9.141

23724

25833

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

9.141

23725

19670

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

9.144

23726

7471

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

9.145

23727

14329

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

9.146

23728

15536

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

9.147

23729

5330

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

9.153

23730

12947

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

9.157

23731

17066

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

9.161

23732

26661

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

9.167

23733

6311

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

9.170

23734

26294

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

9.171

23735

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*}

9.175

23736

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*}

9.177

23737

2953

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

9.183

23738

26249

\begin{align*} x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {5 \pi }{4} \\ \end{align*}

9.183

23739

20283

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

9.184

23740

12161

\begin{align*} y^{\prime }&=\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 y^{2} x^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \\ \end{align*}

9.185

23741

4322

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

9.189

23742

5224

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

9.190

23743

26865

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

9.193

23744

2985

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

9.207

23745

19250

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

9.207

23746

25008

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

9.212

23747

4948

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

9.216

23748

6921

\begin{align*} y+7+\left (2 x +y+3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

9.218

23749

3052

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

9.222

23750

5586

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

9.223

23751

5894

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

9.226

23752

26381

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

9.231

23753

1200

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

9.232

23754

1231

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

9.233

23755

17344

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

9.235

23756

105

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

9.239

23757

12948

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

9.240

23758

17717

\begin{align*} y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}&=0 \\ \end{align*}

Series expansion around \(x=0\).

9.240

23759

20547

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

9.242

23760

5089

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

9.243

23761

23866

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

9.243

23762

15456

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

9.244

23763

15960

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

9.244

23764

19423

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

9.244

23765

13358

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

9.245

23766

22756

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{2}+16 \ln \left (x \right )^{2} \\ \end{align*}

9.246

23767

3030

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

9.247

23768

26398

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

9.247

23769

16306

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

9.253

23770

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*}

9.260

23771

7513

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

9.263

23772

27346

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

9.263

23773

11510

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

9.265

23774

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*}

9.267

23775

22438

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

9.270

23776

7476

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

9.276

23777

16757

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

9.278

23778

23018

\begin{align*} x^{\prime \prime }+36 x&=0 \\ x \left (0\right ) &= 5 \\ x \left (\frac {\pi }{12}\right ) &= 7 \\ \end{align*}

9.279

23779

11562

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

9.283

23780

26330

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

9.288

23781

27564

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

9.288

23782

4890

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

9.294

23783

5272

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

9.297

23784

8697

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

9.300

23785

3555

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

9.302

23786

3672

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

9.308

23787

1803

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

9.309

23788

6983

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

9.309

23789

8256

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

9.310

23790

12386

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

9.313

23791

19859

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

9.314

23792

1205

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

9.319

23793

25717

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (2\right ) &= -3 \\ \end{align*}

9.328

23794

21395

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

9.330

23795

22957

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

9.332

23796

1636

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

9.333

23797

8266

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

9.334

23798

4819

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

9.336

23799

20318

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

9.343

23800

9042

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

9.351