2.3.183 Problems 18201 to 18300

Table 2.909: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

18201

23226

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

3.492

18202

5541

\begin{align*} x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\ \end{align*}

3.493

18203

5808

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

3.493

18204

10108

\begin{align*} y^{\prime \prime }-y x -x^{6}+64&=0 \\ \end{align*}

3.493

18205

4911

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

3.495

18206

15597

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

3.495

18207

15871

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

3.495

18208

17646

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

3.495

18209

5660

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

3.496

18210

22040

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

3.496

18211

752

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

3.497

18212

21088

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

3.497

18213

22079

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

3.497

18214

776

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

3.498

18215

5715

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

3.499

18216

14968

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

3.499

18217

23301

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

3.499

18218

24184

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

3.499

18219

11373

\begin{align*} y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right )&=0 \\ \end{align*}

3.500

18220

15449

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

3.500

18221

13489

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

3.501

18222

9089

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

3.502

18223

2104

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

3.503

18224

24960

\begin{align*} y^{4} y^{\prime }&=t +2 \\ \end{align*}

3.503

18225

17670

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

3.504

18226

1822

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

3.505

18227

25533

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

3.505

18228

18563

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

3.506

18229

19597

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

3.506

18230

21059

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

3.506

18231

24242

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

3.506

18232

10428

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

3.507

18233

2064

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

3.509

18234

1146

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

3.510

18235

17475

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

3.510

18236

19919

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

3.510

18237

22490

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

3.510

18238

4615

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

3.511

18239

15925

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

3.513

18240

7320

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=8 x^{4} \\ \end{align*}

3.515

18241

11331

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

3.515

18242

25046

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

3.515

18243

9050

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

3.516

18244

17135

\begin{align*} y^{\prime }&=16 y-8 y^{2} \\ \end{align*}

3.516

18245

19928

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

3.516

18246

13936

\begin{align*} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}

3.517

18247

16197

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

3.517

18248

18060

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

3.517

18249

13889

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

3.518

18250

6562

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

3.519

18251

11663

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

3.519

18252

19326

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

3.520

18253

19682

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

3.520

18254

22585

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

3.520

18255

2074

\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

3.523

18256

16278

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

3.525

18257

86

\begin{align*} y^{\prime } x -3 y&=x^{3} \\ y \left (1\right ) &= 10 \\ \end{align*}

3.527

18258

8274

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

3.527

18259

22620

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

3.528

18260

19403

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

3.529

18261

22002

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

3.529

18262

146

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

3.530

18263

8777

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

3.531

18264

25042

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

3.531

18265

7680

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

3.532

18266

20026

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

3.532

18267

20027

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

3.532

18268

4202

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

3.533

18269

17150

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

3.533

18270

7481

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

3.535

18271

17930

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

3.535

18272

20234

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

3.535

18273

23105

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

3.535

18274

2062

\begin{align*} 2 x^{2} \left (2+x \right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

3.536

18275

3010

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

3.536

18276

12882

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

3.536

18277

21457

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

3.536

18278

21832

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

3.537

18279

17848

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

3.538

18280

20218

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

3.538

18281

8397

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

3.539

18282

17620

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \\ \end{align*}

3.539

18283

24225

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

3.539

18284

2510

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

3.540

18285

10435

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

3.540

18286

19252

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

3.540

18287

5036

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

3.542

18288

20428

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

3.543

18289

8663

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

3.544

18290

9207

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

3.544

18291

7442

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

3.546

18292

14835

\begin{align*} t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x&=0 \\ \end{align*}

3.546

18293

17180

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

3.546

18294

4728

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

3.547

18295

15634

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

3.547

18296

715

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

3.548

18297

2683

\begin{align*} y^{\prime \prime }+y&=\left \{\begin {array}{cc} 2 & 0\le t \le 3 \\ 3 t -7 & 3<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

3.549

18298

20223

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

3.549

18299

20835

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

3.549

18300

4201

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

3.550