2.3.145 Problems 14401 to 14500

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

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14401

3240

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

1.028

14402

9908

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

1.028

14403

14823

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

1.028

14404

1295

\begin{align*} t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4}&=0 \\ \end{align*}

1.029

14405

5363

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

1.029

14406

15718

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.029

14407

21685

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

1.029

14408

1102

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

1.030

14409

8650

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=\delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

1.030

14410

9885

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

1.030

14411

11710

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

1.030

14412

15030

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

1.030

14413

15407

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

1.030

14414

19615

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

1.030

14415

21525

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

1.030

14416

11733

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

1.031

14417

20539

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

1.031

14418

2563

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

1.032

14419

4574

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

1.032

14420

5747

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

1.032

14421

13730

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

1.032

14422

20456

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

1.032

14423

4611

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

1.033

14424

5979

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

1.033

14425

6982

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

1.033

14426

8187

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align*}

1.033

14427

14413

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

1.033

14428

25574

\begin{align*} 4 a y^{\prime \prime }+b y^{\prime }+\frac {c y}{4}&=f \left (t \right ) \\ \end{align*}

1.033

14429

8668

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

1.034

14430

9954

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

1.034

14431

23180

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

1.034

14432

9951

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

1.035

14433

24837

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

1.035

14434

1278

\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}

1.036

14435

3249

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

1.036

14436

3446

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

1.036

14437

6809

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

1.036

14438

16562

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +29 y&=0 \\ \end{align*}

1.036

14439

17593

\begin{align*} y^{\prime \prime \prime }+9 y^{\prime }&=\sec \left (3 t \right ) \\ \end{align*}

1.036

14440

21803

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

1.036

14441

21871

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

1.036

14442

22349

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

1.036

14443

13764

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

1.037

14444

1354

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

1.038

14445

8872

\begin{align*} L y^{\prime }+R y&=E \\ y \left (0\right ) &= 0 \\ \end{align*}

1.038

14446

22577

\begin{align*} r^{\prime }&={\mathrm e}^{t}-3 r \\ r \left (0\right ) &= 1 \\ \end{align*}

1.038

14447

726

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

1.039

14448

8864

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

1.039

14449

9940

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

1.039

14450

20492

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

1.039

14451

23585

\begin{align*} x^{\prime }&=3 x-2 y+2 t^{2} \\ y^{\prime }&=5 x+y-1 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= {\frac {534}{2197}} \\ y \left (0\right ) &= {\frac {567}{2197}} \\ \end{align*}

1.039

14452

7361

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

1.040

14453

9735

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

1.040

14454

15878

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

1.040

14455

25756

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

1.040

14456

15764

\begin{align*} y_{1}^{\prime }&=3 y_{1}+2 y_{2} \\ y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\ y_{3}^{\prime }&=y_{3} \\ y_{4}^{\prime }&=2 y_{4} \\ \end{align*}

1.041

14457

21755

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

1.041

14458

22804

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

1.041

14459

25198

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

1.041

14460

10226

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

1.042

14461

17667

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

1.042

14462

3964

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

1.043

14463

7417

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

1.043

14464

11303

\begin{align*} y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \\ \end{align*}

1.043

14465

18100

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

1.043

14466

18153

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

1.043

14467

18740

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

1.044

14468

18930

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.044

14469

25406

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

1.044

14470

15617

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

1.045

14471

19415

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

1.045

14472

19778

\begin{align*} v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\ \end{align*}

1.045

14473

21234

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

1.045

14474

22616

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

1.045

14475

25573

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

1.045

14476

230

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

1.046

14477

822

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

1.046

14478

1616

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

1.046

14479

1638

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

1.046

14480

5484

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

1.046

14481

14370

\begin{align*} x^{\prime \prime }+4 x&=\delta \left (t -2\right )-\delta \left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.046

14482

16892

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

1.046

14483

21987

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

1.046

14484

23138

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

1.046

14485

991

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2} \\ x_{3}^{\prime }&=3 x_{2}+3 x_{3} \\ x_{4}^{\prime }&=4 x_{3}+4 x_{4} \\ \end{align*}

1.047

14486

5976

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

1.047

14487

7135

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

1.047

14488

9706

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

1.047

14489

10039

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

1.047

14490

21696

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

1.047

14491

5243

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

1.048

14492

7608

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

1.048

14493

21002

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

1.048

14494

25810

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

1.048

14495

1338

\begin{align*} y^{\prime \prime }+9 y&=9 \sec \left (3 t \right )^{2} \\ \end{align*}

1.049

14496

2177

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+2 y^{\prime }-2 y&={\mathrm e}^{2 x} \left (\left (-x^{2}+5 x +27\right ) \cos \left (x \right )+\left (9 x^{2}+13 x +2\right ) \sin \left (x \right )\right ) \\ \end{align*}

1.049

14497

6422

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

1.049

14498

7964

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

1.049

14499

21904

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

1.049

14500

24266

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

1.049