2.3.143 Problems 14201 to 14300

Table 2.817: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14201

15166

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

0.987

14202

16478

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

0.987

14203

22024

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

0.987

14204

1254

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

0.988

14205

23565

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

0.988

14206

5732

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

0.989

14207

12975

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

0.989

14208

14025

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

0.989

14209

16745

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=18 \ln \left (x \right ) \\ \end{align*}

0.989

14210

18801

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

0.989

14211

23019

\begin{align*} y^{\prime \prime }+3 y&=0 \\ y \left (0\right ) &= 0 \\ y \left (\frac {\pi \sqrt {3}}{6}\right ) &= 4 \\ \end{align*}

0.989

14212

2392

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

0.990

14213

8805

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

0.990

14214

9942

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

0.990

14215

9957

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

0.990

14216

17662

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

0.990

14217

22996

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

0.990

14218

25021

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

0.990

14219

7953

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

0.991

14220

13738

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

0.991

14221

13744

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

0.991

14222

4580

\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2}-x_{3} \\ x_{2}^{\prime }&=-x_{1}+x_{2}+x_{3}+12 t \\ x_{3}^{\prime }&=x_{1}-x_{3} \\ \end{align*}

0.992

14223

18310

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

0.992

14224

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*}

0.992

14225

18850

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

0.992

14226

3222

\begin{align*} 4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y&=0 \\ \end{align*}

0.993

14227

16958

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

0.993

14228

20474

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

0.993

14229

22634

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

0.993

14230

23134

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

0.993

14231

9955

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

0.994

14232

15237

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.994

14233

15391

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

0.994

14234

15540

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

0.994

14235

15768

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

0.994

14236

17179

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

0.994

14237

17373

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

0.994

14238

19620

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

0.995

14239

20661

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

0.995

14240

22558

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

0.995

14241

3865

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

0.996

14242

4273

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

0.996

14243

14985

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

0.996

14244

19047

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

0.996

14245

20384

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

0.996

14246

23378

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

0.996

14247

25572

\begin{align*} m y^{\prime \prime }+k y&=\cos \left (\sqrt {\frac {k}{m}}\, t \right ) \\ \end{align*}

0.996

14248

1298

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

0.997

14249

5619

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

0.997

14250

7687

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

0.997

14251

8733

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

0.997

14252

14933

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

0.997

14253

17031

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

0.997

14254

20741

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

0.997

14255

23338

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

0.997

14256

5666

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

0.998

14257

8104

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

0.998

14258

14316

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

0.998

14259

20720

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

0.998

14260

1297

\begin{align*} t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ \end{align*}

0.999

14261

2705

\begin{align*} x^{\prime }&=4 x+5 y+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ y^{\prime }&=-2 x-2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.999

14262

8261

\begin{align*} y^{\prime \prime }+9 y&=18 \\ \end{align*}

0.999

14263

13703

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

0.999

14264

14257

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

0.999

14265

16973

\begin{align*} x^{2} y^{\prime \prime }-12 y^{\prime } x +42 y&=0 \\ \end{align*}

0.999

14266

19437

\begin{align*} x^{2} y^{\prime \prime }-2 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 8 \\ \end{align*}

0.999

14267

3541

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

1.000

14268

9873

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

1.000

14269

15119

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

1.000

14270

17624

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\ \end{align*}

1.001

14271

19005

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

1.001

14272

21194

\begin{align*} x^{\left (5\right )}+x&=0 \\ x \left (\infty \right ) &= 0 \\ \end{align*}

1.001

14273

21225

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

1.001

14274

24754

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

1.001

14275

6890

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

1.002

14276

4268

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

1.003

14277

18808

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

1.003

14278

20851

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

1.003

14279

22582

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

1.003

14280

18875

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

1.004

14281

9862

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

1.005

14282

9918

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

1.005

14283

9919

\begin{align*} x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.005

14284

18224

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

1.005

14285

25461

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

1.005

14286

15316

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

1.006

14287

15323

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.006

14288

20636

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

1.006

14289

23474

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

1.006

14290

8861

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

1.007

14291

18633

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

1.007

14292

20431

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

1.007

14293

25301

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

1.007

14294

378

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

1.008

14295

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*}

1.008

14296

2606

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

1.008

14297

14882

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

1.008

14298

17487

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

1.008

14299

19008

\begin{align*} x_{1}^{\prime }&=-4 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }&=-6 x_{1}-3 x_{3} \\ x_{3}^{\prime }&=\frac {8 x_{2}}{3}-2 x_{3} \\ \end{align*}

1.008

14300

20097

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

1.008