2.3.124 Problems 12301 to 12400

Table 2.821: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12301

23059

\begin{align*} r r^{\prime }&=a \\ r \left (0\right ) &= b \\ \end{align*}

1.034

12302

8093

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

Series expansion around \(x=0\).

1.035

12303

20906

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

Series expansion around \(x=0\).

1.035

12304

662

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

1.036

12305

698

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

1.036

12306

1239

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

1.036

12307

1993

\begin{align*} 9 x^{2} \left (5+x \right ) y^{\prime \prime }+9 x \left (5+9 x \right ) y^{\prime }-\left (5-8 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.036

12308

2009

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.036

12309

4388

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

1.036

12310

6044

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

1.036

12311

7850

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

1.036

12312

14156

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

1.036

12313

14683

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

1.036

12314

22196

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

Series expansion around \(x=-2\).

1.036

12315

25345

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

Series expansion around \(t=0\).

1.036

12316

27102

\(\left [\begin {array}{cccc} -4 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 1 & 0 & 0 & 3 \end {array}\right ]\)

N/A

N/A

N/A

1.036

12317

1296

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y&=0 \\ \end{align*}

1.037

12318

1952

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

Series expansion around \(x=0\).

1.037

12319

2291

\begin{align*} y_{1}^{\prime }&=2 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }&=y_{2}+y_{3} \\ y_{3}^{\prime }&=y_{1}+y_{3} \\ \end{align*}

1.037

12320

3878

\begin{align*} x_{1}^{\prime }&=-x_{1}-2 x_{2}+2 x_{3}-{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=2 x_{1}+4 x_{2}-x_{3}+4 \,{\mathrm e}^{3 t} \\ x_{3}^{\prime }&=3 x_{3}+3 \,{\mathrm e}^{3 t} \\ \end{align*}

1.037

12321

12469

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

1.037

12322

24589

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

1.037

12323

2063

\begin{align*} x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.038

12324

13254

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

1.038

12325

19157

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

1.038

12326

664

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

1.039

12327

6763

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

1.039

12328

9426

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

Series expansion around \(x=0\).

1.039

12329

13882

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

1.039

12330

14076

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

1.039

12331

1945

\begin{align*} 3 x^{2} y^{\prime \prime }+2 x \left (-2 x^{2}+x +1\right ) y^{\prime }+\left (-8 x^{2}+2 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.040

12332

3706

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

1.040

12333

8590

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

Series expansion around \(x=0\).

1.040

12334

19618

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

Series expansion around \(x=-1\).

1.040

12335

19863

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

1.040

12336

4685

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

1.041

12337

8110

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

Series expansion around \(x=0\).

1.041

12338

9334

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

1.041

12339

15274

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

1.041

12340

16242

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

1.041

12341

24670

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

1.041

12342

27161

\begin{align*} x_{1}^{\prime }&=2 x_{1}+5 x_{2}+6 x_{3} \\ x_{2}^{\prime }&=8 x_{2}+9 x_{3} \\ x_{3}^{\prime }&=x_{2}-2 x_{3} \\ \end{align*}

1.041

12343

27367

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

1.041

12344

10390

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

1.042

12345

1805

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

1.043

12346

3507

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

Series expansion around \(z=0\).

1.043

12347

26185

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

1.043

12348

27370

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

1.043

12349

1946

\begin{align*} x^{2} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+x \left (7 x^{2}+8 x +5\right ) y^{\prime }-\left (-9 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.044

12350

2652

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

Series expansion around \(t=0\).

1.044

12351

3750

\begin{align*} y^{\prime \prime }+9 y&=\frac {36}{4-\cos \left (3 x \right )^{2}} \\ \end{align*}

1.044

12352

4178

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

Series expansion around \(x=0\).

1.044

12353

6648

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

1.044

12354

15040

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

1.044

12355

15885

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

1.044

12356

20484

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

1.044

12357

23543

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

1.044

12358

2080

\begin{align*} 4 x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (7+5 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.045

12359

16049

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

1.045

12360

18435

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

With initial conditions

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

1.045

12361

150

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

1.046

12362

4547

\begin{align*} x^{\prime }-5 x+3 y&=2 \,{\mathrm e}^{3 t} \\ -x+y^{\prime }-y&=5 \,{\mathrm e}^{-t} \\ \end{align*}

1.046

12363

6613

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

1.046

12364

9708

\begin{align*} x^{\prime }&=2 x+3 y-7 \\ y^{\prime }&=-x-2 y+5 \\ \end{align*}

1.046

12365

10265

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

1.046

12366

18253

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

1.046

12367

18642

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

1.046

12368

22159

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

1.046

12369

3133

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

1.047

12370

5725

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

1.047

12371

8045

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

1.047

12372

14735

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

Series expansion around \(x=0\).

1.048

12373

1537

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

1.049

12374

1641

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

1.049

12375

4749

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

1.049

12376

6251

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

1.049

12377

19504

\begin{align*} y^{\prime \prime }+y^{\prime }&=10 x^{4}+2 \\ \end{align*}

1.049

12378

20385

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

1.049

12379

21117

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

1.049

12380

21871

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

1.049

12381

22167

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

1.049

12382

4056

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

Series expansion around \(x=0\).

1.050

12383

10369

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

1.050

12384

20856

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

1.050

12385

21854

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

1.050

12386

8392

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

1.051

12387

14786

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

1.051

12388

16917

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

Series expansion around \(x=0\).

1.051

12389

20211

\begin{align*} 4 x^{\prime }+9 y^{\prime }+2 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+x+24 y&=3 \\ \end{align*}

1.051

12390

907

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

1.052

12391

4036

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

Series expansion around \(x=0\).

1.052

12392

9335

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

1.052

12393

15849

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

1.052

12394

9423

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

Series expansion around \(x=0\).

1.053

12395

16705

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

1.053

12396

18851

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

1.053

12397

1968

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.054

12398

4176

\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=-y_{1}+y_{3} \\ y_{3}^{\prime }&=-y_{2} \\ \end{align*}

1.054

12399

4544

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

1.054

12400

9577

\begin{align*} 4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y&=0 \\ \end{align*}

1.054