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

19018

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

1.828

15202

22761

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

1.828

15203

22862

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

Series expansion around \(r=0\).

1.828

15204

17179

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

1.829

15205

20173

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

1.829

15206

9584

\begin{align*} 16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y&=0 \\ \end{align*}

1.830

15207

11314

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

1.830

15208

20664

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

1.831

15209

25397

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

1.831

15210

4583

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

1.832

15211

6394

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

1.832

15212

8284

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

1.832

15213

9968

\begin{align*} x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.832

15214

13716

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

1.832

15215

14933

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

1.832

15216

22700

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

1.832

15217

2636

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

1.833

15218

5713

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

1.833

15219

9415

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

Series expansion around \(x=-1\).

1.833

15220

15311

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

Series expansion around \(x=0\).

1.834

15221

27288

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

1.834

15222

668

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

1.835

15223

5630

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

1.835

15224

9859

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

Series expansion around \(x=0\).

1.835

15225

20414

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

1.835

15226

20918

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

Using Laplace transform method.

1.835

15227

3271

\begin{align*} y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\ y \left (0\right ) &= \frac {\pi }{4} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.836

15228

3325

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

1.836

15229

6520

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

1.836

15230

8981

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

1.836

15231

18866

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

1.836

15232

6

\begin{align*} y^{\prime }&=x \sqrt {x^{2}+9} \\ y \left (-4\right ) &= 0 \\ \end{align*}

1.837

15233

11419

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

1.837

15234

18943

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

Using Laplace transform method.

1.837

15235

1254

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

1.838

15236

14140

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

1.838

15237

9775

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

1.839

15238

13274

\begin{align*} x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+b \,x^{n} y+c \,x^{m}+d \\ \end{align*}

1.839

15239

20631

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

1.839

15240

22786

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

1.839

15241

24902

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

1.839

15242

26183

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

1.839

15243

1355

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

1.840

15244

3578

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

1.840

15245

5841

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

1.840

15246

15095

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

1.840

15247

4138

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

1.841

15248

5571

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

1.841

15249

8175

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

1.842

15250

21566

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

1.842

15251

26177

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

1.842

15252

3959

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

Using Laplace transform method.

1.843

15253

19461

\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}

1.843

15254

25300

\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (-3+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.843

15255

6987

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

1.844

15256

8216

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

1.844

15257

13789

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

1.844

15258

15899

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

1.844

15259

19128

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

1.844

15260

3131

\begin{align*} y^{\prime \prime }+9 y&=\left (1+\sin \left (3 x \right )\right ) \cos \left (2 x \right ) \\ \end{align*}

1.845

15261

5823

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

1.845

15262

24074

\begin{align*} y^{\left (6\right )}+y&=x^{7}+2 x^{3} \\ \end{align*}

1.845

15263

27085

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

1.845

15264

20321

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

1.846

15265

16154

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

1.849

15266

19992

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

1.849

15267

10229

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

1.850

15268

11329

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

1.850

15269

14937

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

1.850

15270

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.

1.850

15271

15251

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

Using Laplace transform method.

1.851

15272

15722

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=\left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.851

15273

6206

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

1.852

15274

12846

\begin{align*} y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \\ \end{align*}

1.852

15275

9052

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

1.853

15276

15928

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

1.854

15277

2758

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

1.855

15278

3278

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

1.855

15279

7973

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

1.855

15280

9864

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

Series expansion around \(x=0\).

1.855

15281

12396

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

1.855

15282

19693

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

1.855

15283

22715

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

1.855

15284

26232

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

1.855

15285

2300

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

1.856

15286

8208

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

1.856

15287

6040

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

1.857

15288

24041

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

1.857

15289

5394

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

1.858

15290

5939

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

1.858

15291

14161

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

1.858

15292

15318

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

1.858

15293

15112

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

1.859

15294

17664

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

1.859

15295

22357

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

1.860

15296

663

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

1.861

15297

1612

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

1.861

15298

3979

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

1.861

15299

25414

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

1.861

15300

13764

\begin{align*} x y^{\prime \prime }+\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*}

1.862