2.3.273 Problems 27201 to 27300

Table 2.1119: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

27201

20012

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

86.372

27202

17052

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (4\right ) &= -5 \\ \end{align*}

86.464

27203

24182

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

86.477

27204

13470

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

86.537

27205

5090

\begin{align*} \left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\ \end{align*}

86.715

27206

5185

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

87.181

27207

6441

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

87.310

27208

13551

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

87.310

27209

13866

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

87.341

27210

6330

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

87.363

27211

5194

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

87.370

27212

8771

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

87.442

27213

13552

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

87.598

27214

13542

\begin{align*} y y^{\prime }-y&=20 x +\frac {A}{\sqrt {x}} \\ \end{align*}

87.689

27215

24897

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

87.811

27216

4882

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

87.852

27217

8834

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

88.290

27218

14553

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

88.581

27219

8323

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

88.670

27220

11631

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

89.131

27221

13479

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

89.300

27222

5249

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

89.385

27223

26329

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

89.399

27224

25860

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

89.436

27225

17977

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

89.704

27226

5110

\begin{align*} \left (5-x +6 y\right ) y^{\prime }&=3-x +4 y \\ \end{align*}

89.759

27227

13447

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

89.800

27228

13334

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

89.907

27229

15633

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

89.987

27230

12522

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

90.014

27231

5112

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

90.015

27232

11708

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

90.088

27233

5153

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

90.189

27234

6256

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

90.217

27235

13398

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

90.255

27236

20001

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

90.435

27237

23188

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

90.727

27238

13586

\begin{align*} y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}} \\ \end{align*}

90.870

27239

10031

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

90.918

27240

8833

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

90.939

27241

22559

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

91.246

27242

3322

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

91.718

27243

6585

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

91.757

27244

17906

\begin{align*} {\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\ \end{align*}

91.768

27245

22345

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

91.779

27246

4953

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

91.787

27247

13575

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

91.795

27248

20683

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

91.812

27249

18722

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

91.937

27250

6090

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

92.048

27251

2890

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

92.337

27252

11703

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

92.369

27253

21768

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

92.661

27254

13407

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

92.992

27255

23289

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

93.184

27256

21324

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

93.271

27257

25213

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

93.398

27258

7032

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

93.477

27259

13887

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

93.520

27260

23133

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

93.716

27261

25800

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

93.786

27262

13325

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

93.860

27263

17322

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

93.879

27264

6831

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

93.951

27265

27423

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

94.040

27266

9685

\begin{align*} x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \\ \end{align*}

94.423

27267

26370

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

94.456

27268

5202

\begin{align*} 8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4}&=0 \\ \end{align*}

94.512

27269

13913

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

94.691

27270

6146

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

95.039

27271

13625

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

95.062

27272

6050

\begin{align*} y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

95.135

27273

18051

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

95.180

27274

13606

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

95.444

27275

13616

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

95.445

27276

21449

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

95.566

27277

13339

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

95.595

27278

13612

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

95.601

27279

9820

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

95.624

27280

21789

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

95.723

27281

13278

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

95.883

27282

21464

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

95.954

27283

12565

\begin{align*} \operatorname {A2} \left (a x +b \right )^{2} y^{\prime \prime }+\operatorname {A1} \left (a x +b \right ) y^{\prime }+\operatorname {A0} \left (a x +b \right ) y&=0 \\ \end{align*}

96.189

27284

20723

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

96.226

27285

5295

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

96.299

27286

5122

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

96.440

27287

5152

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

96.493

27288

23199

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

96.533

27289

13349

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

96.599

27290

22020

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

96.681

27291

2918

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

96.760

27292

20433

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

97.241

27293

11816

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

97.479

27294

24155

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

97.486

27295

13896

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

97.529

27296

22466

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

97.595

27297

4748

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

97.709

27298

5121

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

97.866

27299

25891

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

97.901

27300

10063

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

97.989