2.3.222 Problems 22101 to 22200

Table 2.987: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22101

25694

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

9.337

22102

4929

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

9.339

22103

20318

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

9.343

22104

18053

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

9.344

22105

7350

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

9.351

22106

20249

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

9.358

22107

20826

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

9.362

22108

19798

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

9.364

22109

14524

\begin{align*} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\ \end{align*}

9.370

22110

20307

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

9.373

22111

17039

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

9.380

22112

2897

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

9.381

22113

16143

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

9.382

22114

9020

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

9.389

22115

13713

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

9.394

22116

6826

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

9.395

22117

22596

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

9.396

22118

3029

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

9.398

22119

21067

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

9.401

22120

17985

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

9.402

22121

23897

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

9.402

22122

22524

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

9.405

22123

11942

\begin{align*} y^{\prime }&=-\frac {a x}{2}-\frac {b}{2}+x \sqrt {a^{2} x^{2}+2 a b x +b^{2}+4 a y-4 c} \\ \end{align*}

9.406

22124

2947

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

9.407

22125

11996

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

9.408

22126

4928

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

9.413

22127

17068

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

9.414

22128

10318

\begin{align*} y^{\prime }&=\sqrt {1+6 x +y} \\ \end{align*}

9.421

22129

5697

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

9.422

22130

13908

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

9.422

22131

6907

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

9.427

22132

23962

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

9.432

22133

212

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

9.435

22134

11351

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

9.438

22135

7682

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

9.443

22136

6583

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

9.447

22137

15057

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

9.449

22138

12998

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

9.456

22139

10067

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

9.461

22140

7433

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

9.464

22141

11339

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

9.464

22142

4947

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

9.467

22143

23889

\begin{align*} \frac {y^{5} x^{2}+y^{2}+y}{1+x^{2} y^{4}}+\frac {\left (x^{3} y^{4}+2 y x +x \right ) y^{\prime }}{1+x^{2} y^{4}}&=0 \\ \end{align*}

9.471

22144

5812

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

9.474

22145

12420

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

9.475

22146

14464

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

9.475

22147

5043

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

9.479

22148

11705

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

9.483

22149

3549

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

9.490

22150

22959

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

9.490

22151

1199

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

9.496

22152

23161

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

9.497

22153

21734

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

9.501

22154

1164

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

9.507

22155

14890

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

9.510

22156

12991

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

9.511

22157

4849

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

9.512

22158

14888

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

9.519

22159

24175

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

9.527

22160

7483

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

9.541

22161

20816

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

9.542

22162

7396

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

9.556

22163

14486

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

9.557

22164

20474

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

9.559

22165

12263

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

9.563

22166

6992

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

9.567

22167

22395

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

9.570

22168

13221

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

9.576

22169

19310

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

9.576

22170

19767

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

9.578

22171

5332

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

9.582

22172

25469

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

9.584

22173

13427

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

9.590

22174

8717

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

9.598

22175

4691

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

9.601

22176

5231

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

9.603

22177

19250

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

9.604

22178

12061

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

9.607

22179

12055

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

9.611

22180

23157

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

9.611

22181

17088

\begin{align*} y^{\prime }&=\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \\ \end{align*}

9.612

22182

26251

\begin{align*} x^{3} y^{\prime }-\cos \left (y\right )&=1 \\ y \left (\infty \right ) &= 5 \pi \\ \end{align*}

9.613

22183

7476

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

9.631

22184

24342

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

9.631

22185

5333

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

9.633

22186

4993

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

9.638

22187

5049

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

9.638

22188

17144

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

9.640

22189

11607

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

9.641

22190

7017

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

9.642

22191

8403

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

9.644

22192

15158

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

9.649

22193

23855

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

9.649

22194

17975

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

9.659

22195

12081

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

9.661

22196

19288

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

9.664

22197

4956

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

9.668

22198

105

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

9.674

22199

9157

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

9.679

22200

5599

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

9.685