2.3.262 Problems 26101 to 26200

Table 2.1097: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

26101

5214

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

32.967

26102

6914

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

32.970

26103

4789

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

33.003

26104

25888

\begin{align*} 3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\ \end{align*}

33.015

26105

5148

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

33.029

26106

12851

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

33.035

26107

2993

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

33.083

26108

17290

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

33.141

26109

5686

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

33.154

26110

11553

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

33.186

26111

24406

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

33.193

26112

19966

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

33.201

26113

4778

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

33.205

26114

22551

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

33.207

26115

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*}

33.221

26116

27002

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

33.243

26117

5987

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

33.327

26118

6833

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

33.329

26119

6846

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

33.351

26120

17324

\begin{align*} x^{\prime }&=\frac {5 t x}{t^{2}+x^{2}} \\ \end{align*}

33.369

26121

7848

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

33.371

26122

24376

\begin{align*} y \left (8 x -9 y\right )+2 x \left (x -3 y\right ) y^{\prime }&=0 \\ \end{align*}

33.421

26123

22609

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

33.440

26124

19309

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

33.441

26125

5376

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

33.445

26126

21062

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

33.448

26127

5628

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

33.454

26128

26692

\begin{align*} y^{\prime \prime }&=\alpha ^{2} s^{2} y+\alpha ^{2} g L \\ y \left (0\right ) &= 0 \\ y \left (x_{0} \right ) &= 0 \\ \end{align*}

33.458

26129

13210

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

33.462

26130

22388

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

33.470

26131

26688

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

33.503

26132

2933

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

33.514

26133

6415

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

33.559

26134

5260

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

33.581

26135

13809

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

33.698

26136

20274

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

33.743

26137

6965

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

33.763

26138

5170

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

33.785

26139

20400

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

33.810

26140

27005

\begin{align*} x^{2} y^{\prime \prime }-11 x y^{\prime }+35 y&=0 \\ \end{align*}

33.829

26141

2507

\begin{align*} 1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime }&=0 \\ \end{align*}

33.849

26142

5749

\begin{align*} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime }&=0 \\ \end{align*}

33.862

26143

13331

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

33.864

26144

5938

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (x +a \right ) y^{\prime \prime }&=0 \\ \end{align*}

33.888

26145

4243

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

33.927

26146

25016

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

33.937

26147

13036

\begin{align*} \left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 {y^{\prime }}^{2} x&=0 \\ \end{align*}

33.940

26148

6820

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

33.944

26149

5702

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

33.982

26150

27247

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

33.993

26151

5343

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

34.039

26152

5706

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

34.051

26153

5264

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

34.059

26154

13287

\begin{align*} y^{\prime }&=y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4} \\ \end{align*}

34.092

26155

15055

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

34.110

26156

8723

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

34.211

26157

11792

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

34.230

26158

12867

\begin{align*} y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b&=0 \\ \end{align*}

34.242

26159

24064

\begin{align*} y^{\left (10\right )}+y&=x^{10} \\ \end{align*}

34.253

26160

24380

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

34.342

26161

6980

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

34.345

26162

16337

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

34.374

26163

14866

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

34.396

26164

6979

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

34.484

26165

22529

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

34.497

26166

13471

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

34.543

26167

19458

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

34.577

26168

11912

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

34.607

26169

15036

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

34.610

26170

25708

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

34.611

26171

6826

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

34.625

26172

20294

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

34.628

26173

9080

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

34.647

26174

27250

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

34.667

26175

7560

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

34.668

26176

24132

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

34.673

26177

6992

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

34.682

26178

26621

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

34.692

26179

5169

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

34.750

26180

24404

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

34.754

26181

6302

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

34.771

26182

9054

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

34.799

26183

12113

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

34.824

26184

7486

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

34.831

26185

22396

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

34.838

26186

6461

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

34.848

26187

20280

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

34.904

26188

12093

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

34.917

26189

20695

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

34.928

26190

24358

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

34.934

26191

20252

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

34.981

26192

5168

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

35.006

26193

6025

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

35.067

26194

4788

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

35.074

26195

17948

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

35.088

26196

23960

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

35.100

26197

17038

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

35.115

26198

13441

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

35.202

26199

12240

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

35.214

26200

4357

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

35.250