2.3.83 Problems 8201 to 8300

Table 2.739: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8201

27529

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

0.604

8202

1847

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

Series expansion around \(x=1\).

0.605

8203

1903

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

Series expansion around \(x=1\).

0.605

8204

2584

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

0.605

8205

3429

\begin{align*} y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \\ y \left (0\right ) &= 12 \\ \end{align*}

0.605

8206

3797

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=4 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.605

8207

3997

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

Series expansion around \(x=0\).

0.605

8208

5456

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

0.605

8209

7660

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

Series expansion around \(x=0\).

0.605

8210

7805

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

0.605

8211

8797

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

0.605

8212

8911

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

0.605

8213

9232

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.605

8214

10140

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

0.605

8215

12277

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

0.605

8216

16108

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

0.605

8217

17377

\begin{align*} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y&=0 \\ \end{align*}

0.605

8218

17536

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

0.605

8219

17595

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

0.605

8220

17693

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

Series expansion around \(x=0\).

0.605

8221

20144

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

0.605

8222

21519

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=2 x^{3}+5 x^{2}-7 x +2 \\ \end{align*}

0.605

8223

22278

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

0.605

8224

23063

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

0.605

8225

24579

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

0.605

8226

24668

\begin{align*} y^{\prime \prime }+16 y&=48 \cos \left (4 x \right ) \\ \end{align*}

0.605

8227

24680

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

0.605

8228

25373

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

With initial conditions

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

0.605

8229

876

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

0.606

8230

3214

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

0.606

8231

3488

\begin{align*} f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= -2 \\ \end{align*}

0.606

8232

3585

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

0.606

8233

4649

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

0.606

8234

7086

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

0.606

8235

7779

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

0.606

8236

9318

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

0.606

8237

13153

\(\left [\begin {array}{ccc} 1 & 0 & -1 \\ -2 & 3 & -1 \\ -6 & 6 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.606

8238

13190

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

N/A

N/A

N/A

0.606

8239

13196

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

N/A

N/A

N/A

0.606

8240

14581

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

0.606

8241

15684

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \\ \end{align*}

0.606

8242

16861

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

Series expansion around \(x=2\).

0.606

8243

17692

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

Series expansion around \(x=0\).

0.606

8244

17809

\begin{align*} 4 x^{\prime \prime }+2 x^{\prime }+8 x&=0 \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.606

8245

21747

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

With initial conditions

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

0.606

8246

22261

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

With initial conditions

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

0.606

8247

23091

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

0.606

8248

24708

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \cos \left (3 x \right ) \\ \end{align*}

0.606

8249

841

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

0.607

8250

7641

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

Series expansion around \(x=1\).

0.607

8251

8488

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

Series expansion around \(x=0\).

0.607

8252

9466

\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

0.607

8253

12477

\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*}

0.607

8254

14523

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

0.607

8255

15472

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

0.607

8256

16609

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-5 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

0.607

8257

23528

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

0.607

8258

25141

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

0.607

8259

25942

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

0.607

8260

25980

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

0.607

8261

3737

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=40 \sin \left (x \right )^{2} \\ \end{align*}

0.608

8262

4129

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

0.608

8263

6300

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

0.608

8264

7107

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

0.608

8265

7406

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

0.608

8266

8005

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

0.608

8267

9332

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

0.608

8268

15716

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

Using Laplace transform method.

0.608

8269

18211

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

0.608

8270

21739

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

0.608

8271

22249

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

Using Laplace transform method.

0.608

8272

23604

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

0.608

8273

24679

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

0.608

8274

25599

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

0.608

8275

25990

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

0.608

8276

27586

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

0.608

8277

337

\begin{align*} y^{\prime \prime }+9 y&=2 x^{2} {\mathrm e}^{3 x}+5 \\ \end{align*}

0.609

8278

566

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

Using Laplace transform method.

0.609

8279

1898

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

Series expansion around \(x=1\).

0.609

8280

7627

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

Series expansion around \(x=0\).

0.609

8281

7642

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

Series expansion around \(x=0\).

0.609

8282

9696

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

0.609

8283

10419

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

0.609

8284

21165

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

0.609

8285

21740

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

0.609

8286

21883

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

0.609

8287

24562

\begin{align*} y^{\prime \prime }-4 y&=2-8 x \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.609

8288

24624

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \\ \end{align*}

0.609

8289

24667

\begin{align*} y^{\prime \prime }+16 y&=24 \sin \left (4 x \right ) \\ \end{align*}

0.609

8290

25945

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

0.609

8291

584

\begin{align*} x^{\prime }&=-y \\ y^{\prime }&=13 x+4 y \\ \end{align*}

With initial conditions

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

0.610

8292

635

\begin{align*} x_{1}^{\prime }&=7 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=4 x_{1}+3 x_{2} \\ \end{align*}

0.610

8293

8570

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

Series expansion around \(x=0\).

0.610

8294

9670

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

0.610

8295

16119

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

0.610

8296

20101

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

0.610

8297

21572

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

0.610

8298

24656

\begin{align*} y^{\prime \prime }+36 y&=\cos \left (6 x \right ) \\ \end{align*}

0.610

8299

374

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

0.611

8300

3182

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

0.611