2.3.94 Problems 9301 to 9400

Table 2.719: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9301

7603

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

0.995

9302

12719

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

0.995

9303

9994

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

0.996

9304

13025

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

0.996

9305

5534

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

0.997

9306

21272

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

0.997

9307

24770

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

0.997

9308

2762

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

0.998

9309

10206

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

0.998

9310

16879

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

0.998

9311

16944

\begin{align*} x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.998

9312

8733

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

0.999

9313

10188

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

0.999

9314

10208

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

0.999

9315

22930

\begin{align*} x^{\prime }-5 x+y^{\prime }+2 z&=24 \,{\mathrm e}^{-t} \\ x^{\prime }-x-y&=0 \\ 5 y^{\prime }-11 y+2 z^{\prime }-2 z&=0 \\ \end{align*}

0.999

9316

2274

\begin{align*} y_{1}^{\prime }&=4 y_{1}-8 y_{2}-4 y_{3} \\ y_{2}^{\prime }&=-3 y_{1}-y_{2}-4 y_{3} \\ y_{3}^{\prime }&=y_{1}-y_{2}+9 y_{3} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= -4 \\ y_{2} \left (0\right ) &= 1 \\ y_{3} \left (0\right ) &= -3 \\ \end{align*}

1.000

9317

2607

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

1.000

9318

2708

\begin{align*} x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\ y^{\prime }&=-x+f_{2} \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

1.000

9319

3842

\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+6 x_{3} \\ x_{2}^{\prime }&=-2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }&=-x_{1}-2 x_{2}-4 x_{3} \\ \end{align*}

1.000

9320

3902

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

1.000

9321

5605

\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a&=0 \\ \end{align*}

1.000

9322

16891

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

1.000

9323

16915

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

1.000

9324

25285

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \\ \end{align*}
Using Laplace transform method.

1.000

9325

25678

\begin{align*} 3 y^{\prime }&=4 y \\ \end{align*}

1.000

9326

2812

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

1.001

9327

9405

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

1.002

9328

25297

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

1.002

9329

1673

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

1.003

9330

6525

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

1.003

9331

8137

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

1.003

9332

10948

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

1.003

9333

17101

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

1.003

9334

6514

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

1.004

9335

7655

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

1.004

9336

8107

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

1.004

9337

8252

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

1.004

9338

10466

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

1.004

9339

24767

\begin{align*} v^{\prime }-2 v+2 w^{\prime }&=2-4 \,{\mathrm e}^{2 x} \\ 2 v^{\prime }-3 v+3 w^{\prime }-w&=0 \\ \end{align*}

1.004

9340

9891

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

1.005

9341

10465

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

1.005

9342

15753

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

1.005

9343

648

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+9 x_{4} \\ x_{2}^{\prime }&=4 x_{1}+2 x_{2}-10 x_{4} \\ x_{3}^{\prime }&=-x_{3}+8 x_{4} \\ x_{4}^{\prime }&=x_{4} \\ \end{align*}

1.006

9344

5667

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

1.006

9345

6519

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

1.006

9346

9429

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

1.006

9347

236

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

1.007

9348

422

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

1.007

9349

2189

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y&={\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \\ \end{align*}

1.007

9350

15458

\begin{align*} x^{\prime }&=2 x-3 y \\ y^{\prime }&=5 x+6 y \\ \end{align*}

1.007

9351

15409

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

1.008

9352

17397

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

1.008

9353

5388

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

1.009

9354

177

\begin{align*} x^{\prime }&=4 x \left (7-x\right ) \\ x \left (0\right ) &= 11 \\ \end{align*}

1.011

9355

8083

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

1.011

9356

12871

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

1.011

9357

12984

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

1.011

9358

21437

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

1.011

9359

8307

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

1.012

9360

16913

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

1.012

9361

22980

\begin{align*} y^{\prime }-6 y&={\mathrm e}^{6 t} \\ y \left (0\right ) &= 0 \\ \end{align*}

1.012

9362

7309

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

1.013

9363

10668

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

1.013

9364

19237

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

1.013

9365

22804

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

1.013

9366

172

\begin{align*} x^{\prime }&=10 x-x^{2} \\ x \left (0\right ) &= 1 \\ \end{align*}

1.014

9367

8136

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

1.014

9368

9427

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

1.014

9369

10178

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

1.014

9370

10704

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

1.014

9371

4438

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

1.015

9372

9551

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

1.015

9373

13009

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

1.015

9374

18639

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

1.015

9375

19006

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

1.015

9376

3240

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

1.016

9377

12104

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

1.017

9378

14186

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

1.017

9379

19886

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

1.017

9380

22926

\begin{align*} 3 x-y^{\prime }-2 y&=8 t \\ x^{\prime }-2 x+y&=16 \,{\mathrm e}^{-t} \\ \end{align*}

1.017

9381

6568

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

1.018

9382

9958

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

1.018

9383

4585

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

1.019

9384

8242

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

1.019

9385

15897

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

1.019

9386

17715

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

1.019

9387

18644

\begin{align*} x^{\prime }&=-2 x+y-11 \\ y^{\prime }&=-5 x+4 y-35 \\ \end{align*}

1.019

9388

19044

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

1.019

9389

2530

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

1.020

9390

7629

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

1.020

9391

14824

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.020

9392

15937

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

1.020

9393

2732

\begin{align*} x_{1}^{\prime }&=x_{1}+2 x_{2}+3 x_{3}+6 x_{4} \\ x_{2}^{\prime }&=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4} \\ x_{3}^{\prime }&=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4} \\ x_{4}^{\prime }&=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4} \\ \end{align*}

1.021

9394

16142

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

1.021

9395

20464

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

1.021

9396

22753

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

1.021

9397

22783

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

1.021

9398

15371

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

1.022

9399

25423

\begin{align*} y^{\prime }&=-y+\operatorname {Heaviside}\left (t -3\right )+\delta \left (t -1\right ) \\ \end{align*}

1.022

9400

9966

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

1.023