2.3.73 Problems 7201 to 7300

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

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7201

14815

\begin{align*} y^{\prime \prime }+4 y&=8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

Using Laplace transform method.

0.537

7202

15742

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

N/A

N/A

N/A

0.537

7203

16016

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

With initial conditions

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

0.537

7204

18683

\begin{align*} i^{\prime }&=\frac {i}{2}-\frac {v}{8} \\ v^{\prime }&=2 i-\frac {v}{2} \\ \end{align*}

0.537

7205

19245

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

0.537

7206

20419

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

0.537

7207

20789

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

0.537

7208

26573

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

0.537

7209

2571

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 2 \\ \end{align*}

0.538

7210

8088

\begin{align*} z^{\prime \prime }+z^{\prime } t +\left (t^{2}-\frac {1}{9}\right ) z&=0 \\ \end{align*}

Series expansion around \(t=0\).

0.538

7211

8281

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

0.538

7212

8796

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

0.538

7213

9319

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

0.538

7214

13843

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

0.538

7215

18718

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

0.538

7216

23435

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

Series expansion around \(x=0\).

0.538

7217

27580

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

0.538

7218

569

\begin{align*} x^{\prime \prime }+9 x&=\delta \left (t -3 \pi \right )+\cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.539

7219

873

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

0.539

7220

1401

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

0.539

7221

2388

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.539

7222

2559

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

0.539

7223

7312

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

0.539

7224

7906

\begin{align*} y+x^{3} y+2 x^{2}+\left (x +4 x y^{4}+8 y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

0.539

7225

9330

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

0.539

7226

17526

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=65 \cos \left (2 t \right ) \\ \end{align*}

0.539

7227

19051

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

0.539

7228

20938

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

0.539

7229

24459

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

0.539

7230

24632

\begin{align*} y^{\prime \prime }-9 y&=-72 x \,{\mathrm e}^{-3 x} \\ \end{align*}

0.539

7231

27195

\begin{align*} x_{1}^{\prime }&=3 x_{1}-5 x_{2} \\ x_{2}^{\prime }&=8 x_{1}-3 x_{2} \\ \end{align*}

0.539

7232

983

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

0.540

7233

1094

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

Series expansion around \(x=0\).

0.540

7234

1884

\begin{align*} \left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.540

7235

1892

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

Series expansion around \(x=0\).

0.540

7236

3827

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

With initial conditions

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

0.540

7237

7651

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

Series expansion around \(t=0\).

0.540

7238

10153

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

0.540

7239

10225

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

Series expansion around \(x=0\).

0.540

7240

16161

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

0.540

7241

18429

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

0.540

7242

20849

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

0.540

7243

21168

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

0.540

7244

23082

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

0.540

7245

23820

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

0.540

7246

23832

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

0.540

7247

27012

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

Using Laplace transform method.

0.540

7248

7797

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

0.541

7249

14377

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

0.541

7250

14995

\(\left [\begin {array}{cc} 2 & -3 \\ 3 & 2 \end {array}\right ]\)

N/A

N/A

N/A

0.541

7251

24693

\begin{align*} 4 y+y^{\prime \prime }&=8 x^{5} \\ \end{align*}

0.541

7252

26548

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

0.541

7253

26963

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

0.541

7254

27154

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

0.541

7255

913

\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \\ \end{align*}

0.542

7256

2582

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

0.542

7257

2747

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

0.542

7258

4160

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

0.542

7259

7188

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

Series expansion around \(x=0\).

0.542

7260

8473

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

0.542

7261

8635

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=50 t -100 \\ y \left (2\right ) &= -4 \\ y^{\prime }\left (2\right ) &= 14 \\ \end{align*}

Using Laplace transform method.

0.542

7262

9072

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

0.542

7263

9611

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

Using Laplace transform method.

0.542

7264

12973

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

0.542

7265

13197

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

N/A

N/A

N/A

0.542

7266

19404

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

0.542

7267

21082

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

0.542

7268

21647

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

Series expansion around \(x=0\).

0.542

7269

22234

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.542

7270

22678

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

0.542

7271

23449

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

Series expansion around \(x=0\).

0.542

7272

25136

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=\sin \left (t \right ) \\ \end{align*}

0.542

7273

26515

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&={\mathrm e}^{-3 x} \cos \left (2 x \right ) \\ \end{align*}

0.542

7274

3150

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

0.543

7275

4119

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ \end{align*}

0.543

7276

5782

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

0.543

7277

7098

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

0.543

7278

7099

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

0.543

7279

7108

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

0.543

7280

8340

\begin{align*} 1+{\mathrm e}^{3 x} y^{\prime }&=0 \\ \end{align*}

0.543

7281

12903

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

0.543

7282

12985

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

0.543

7283

13705

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

0.543

7284

14397

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

0.543

7285

14635

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

0.543

7286

16089

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

0.543

7287

17702

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

Series expansion around \(x=0\).

0.543

7288

20703

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

0.543

7289

21866

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

0.543

7290

23982

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

0.543

7291

24655

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

0.543

7292

25617

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

0.543

7293

1896

\begin{align*} \left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y&=0 \\ y \left (0\right ) &= 7 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

Series expansion around \(x=0\).

0.544

7294

15524

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

0.544

7295

15836

\begin{align*} v^{\prime }&=\frac {K -v}{R C} \\ \end{align*}

0.544

7296

17425

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=-{\mathrm e}^{-9 t} \\ \end{align*}

0.544

7297

18685

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

0.544

7298

24698

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

0.544

7299

8576

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

Series expansion around \(x=0\).

0.545

7300

8913

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

0.545