2.3.153 Problems 15201 to 15300

Table 2.879: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15201

3429

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

1.448

15202

17429

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

1.448

15203

17839

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

1.448

15204

20617

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

1.448

15205

25458

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

1.448

15206

26197

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

1.448

15207

27385

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

1.448

15208

5533

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

1.449

15209

16570

\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\ y \left (1\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

1.449

15210

25698

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

1.449

15211

904

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

1.450

15212

5983

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

1.450

15213

11407

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

1.450

15214

15371

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

1.450

15215

18001

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

1.450

15216

24076

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

1.450

15217

100

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

1.451

15218

4251

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

1.451

15219

5503

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

1.451

15220

5906

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

1.451

15221

16101

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

1.451

15222

11710

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

1.452

15223

20621

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

1.453

15224

23926

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

1.453

15225

25461

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

1.453

15226

27176

\begin{align*} x_{1}^{\prime }&=6 x_{1}+5 x_{2}-4 \cos \left (3 t \right ) \\ x_{2}^{\prime }&=x_{1}+2 x_{2}+8 \\ \end{align*}

1.453

15227

5441

\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}

1.454

15228

8889

\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}

1.454

15229

10433

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

1.454

15230

17455

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

1.454

15231

26564

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

1.454

15232

5733

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

1.455

15233

18953

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{10}+y&=k \delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.455

15234

14324

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

1.456

15235

25184

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

1.456

15236

13030

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

1.457

15237

23102

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

1.457

15238

1039

\begin{align*} x_{1}^{\prime }&=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }&=3 x_{2} \\ x_{3}^{\prime }&=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }&=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }&=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \\ \end{align*}

1.459

15239

2655

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

Series expansion around \(t=0\).

1.459

15240

5567

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

1.459

15241

7175

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

Series expansion around \(x=0\).

1.459

15242

5855

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

1.460

15243

8641

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.460

15244

19393

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

1.460

15245

19230

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

1.461

15246

4345

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

1.463

15247

5362

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

1.463

15248

9625

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

1.463

15249

21172

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

1.463

15250

4263

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

1.464

15251

14946

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

1.464

15252

4098

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

1.465

15253

4653

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

1.465

15254

5961

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

1.466

15255

20087

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

1.466

15256

20856

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

1.466

15257

26361

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

1.466

15258

1117

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

1.467

15259

12469

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

1.467

15260

26562

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

1.467

15261

15066

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

1.468

15262

25832

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

1.468

15263

9938

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

Series expansion around \(x=0\).

1.469

15264

22939

\begin{align*} x^{\prime }&=-12 x-7 y \\ y^{\prime }&=19 x+11 y \\ \end{align*}

1.469

15265

2689

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

Using Laplace transform method.

1.470

15266

17488

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

1.470

15267

20767

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

1.470

15268

17930

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

1.471

15269

21987

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

1.471

15270

20735

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

1.472

15271

25561

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

1.472

15272

5575

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

1.473

15273

9385

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

Series expansion around \(x=0\).

1.473

15274

16434

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

1.475

15275

6933

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

1.477

15276

8746

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

1.477

15277

14268

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

1.477

15278

15231

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=36 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -1\right )\right ) \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

Using Laplace transform method.

1.477

15279

1288

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

1.478

15280

6409

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

1.478

15281

17279

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

1.478

15282

86

\begin{align*} y^{\prime } x -3 y&=x^{3} \\ y \left (1\right ) &= 10 \\ \end{align*}

1.479

15283

8264

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

1.480

15284

20152

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

1.480

15285

22163

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

1.480

15286

24310

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

1.480

15287

25

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

1.481

15288

24919

\begin{align*} y^{\prime }&=-{\mathrm e}^{y}-1 \\ \end{align*}

1.481

15289

25299

\begin{align*} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

1.481

15290

24070

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

1.482

15291

3440

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

1.483

15292

3441

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

1.483

15293

4216

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

1.483

15294

13108

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

1.483

15295

21562

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

1.483

15296

27377

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

1.483

15297

14264

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

1.484

15298

17329

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

1.484

15299

19854

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

1.484

15300

20008

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

1.485