2.3.84 Problems 8301 to 8400

Table 2.699: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8301

3846

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

0.786

8302

4029

\begin{align*} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.786

8303

6526

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

0.786

8304

10173

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

0.786

8305

10180

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

0.786

8306

10660

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

0.786

8307

12771

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

0.786

8308

16886

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

0.786

8309

17705

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

0.786

8310

25482

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

0.786

8311

1958

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

0.787

8312

2645

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

0.787

8313

10171

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

0.787

8314

20163

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

0.787

8315

22277

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+9 \,{\mathrm e}^{-t} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

0.787

8316

6404

\begin{align*} 24+12 y x +x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\ \end{align*}

0.788

8317

8530

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

0.788

8318

10548

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

0.788

8319

11190

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

0.788

8320

1507

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

0.789

8321

5592

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

0.789

8322

6821

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

0.789

8323

9750

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

0.789

8324

9877

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

0.789

8325

20167

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

0.789

8326

23748

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

0.789

8327

1125

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

0.790

8328

20014

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

0.790

8329

2085

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.791

8330

6429

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

0.791

8331

10169

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

0.791

8332

14598

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.791

8333

16870

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

0.791

8334

17577

\begin{align*} \frac {31 y^{\prime \prime \prime }}{100}+\frac {56 y^{\prime \prime }}{5}-\frac {49 y^{\prime }}{5}+\frac {53 y}{10}&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -1 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

0.791

8335

25414

\begin{align*} y^{\prime }-5 y&=3 \operatorname {Heaviside}\left (t -4\right ) \\ \end{align*}

0.791

8336

8057

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

0.792

8337

24051

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-y^{\prime }+2 y&=-2 x^{4}+x^{2} \\ \end{align*}
Using Laplace transform method.

0.792

8338

9693

\begin{align*} x^{\prime }&=5 x-4 y \\ y^{\prime }&=x+2 z \\ z^{\prime }&=2 y+5 z \\ \end{align*}

0.793

8339

17687

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

0.793

8340

25186

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

0.793

8341

25415

\begin{align*} y+y^{\prime }&=7 \operatorname {Heaviside}\left (t -4\right ) \\ \end{align*}

0.793

8342

1963

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

0.794

8343

2083

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

0.795

8344

3380

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

0.795

8345

6520

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

0.795

8346

7835

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

0.795

8347

8995

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

0.795

8348

20379

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 \cos \left (x \right ) x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 12 \\ \end{align*}

0.795

8349

25341

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

0.795

8350

600

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

0.796

8351

2102

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.796

8352

3904

\begin{align*} x_{1}^{\prime }&=-17 x_{1}-42 x_{3} \\ x_{2}^{\prime }&=-7 x_{1}+4 x_{2}-14 x_{3} \\ x_{3}^{\prime }&=7 x_{1}+18 x_{3} \\ \end{align*}

0.796

8353

8647

\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.796

8354

18938

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

0.796

8355

20851

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

0.796

8356

21547

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

0.796

8357

1454

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

0.797

8358

3364

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

0.797

8359

4548

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

0.797

8360

8593

\begin{align*} 4 y^{\prime \prime } x +y^{\prime }+8 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.797

8361

15835

\begin{align*} v^{\prime }&=-\frac {v}{R C} \\ \end{align*}

0.797

8362

24100

\begin{align*} 25 x^{2} y^{\prime \prime }+\left (2 x +4\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.797

8363

25303

\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -2 \pi \right ) \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.797

8364

8998

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

0.798

8365

1386

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

0.799

8366

1956

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

0.799

8367

1981

\begin{align*} x \left (x^{2}+1\right ) y^{\prime \prime }+\left (7 x^{2}+4\right ) y^{\prime }+8 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.799

8368

8215

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

0.799

8369

10200

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

0.799

8370

10531

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

0.799

8371

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.

0.799

8372

15390

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

0.799

8373

20895

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

0.799

8374

21974

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

0.799

8375

2336

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

0.800

8376

9251

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

0.800

8377

24005

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

0.800

8378

5653

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

0.801

8379

7141

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

0.801

8380

8618

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

0.801

8381

10175

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

0.801

8382

16926

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

0.801

8383

17720

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

0.801

8384

23742

\begin{align*} 2 \left (x +3\right )^{2} y^{\prime \prime }-\left (x^{2}+5 x +6\right ) y^{\prime }-y&=0 \\ \end{align*}
Series expansion around \(x=-3\).

0.801

8385

1978

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

0.802

8386

3365

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

0.802

8387

11141

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

0.802

8388

15315

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

0.802

8389

3354

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

0.803

8390

9002

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

0.803

8391

13055

\begin{align*} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \\ \end{align*}

0.803

8392

15308

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

0.803

8393

21905

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

0.803

8394

24095

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

0.803

8395

1850

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

0.804

8396

4182

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

0.804

8397

4598

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

0.804

8398

7644

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

0.804

8399

15865

\begin{align*} y^{\prime }&=y^{2}-4 y-12 \\ y \left (1\right ) &= 0 \\ \end{align*}

0.804

8400

20207

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

0.804