2.3.93 Problems 9201 to 9300

Table 2.759: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9201

7649

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

Series expansion around \(x=2\).

0.678

9202

10141

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

0.678

9203

10260

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

0.678

9204

12570

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

0.678

9205

16644

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

0.678

9206

16677

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=20 \sinh \left (x \right ) \\ \end{align*}

0.678

9207

16871

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

Series expansion around \(x=1\).

0.678

9208

18459

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

Using Laplace transform method.

0.678

9209

23509

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

0.678

9210

23738

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

Series expansion around \(x=0\).

0.678

9211

24737

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=\frac {6}{1+{\mathrm e}^{-2 x}} \\ \end{align*}

0.678

9212

24765

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

0.678

9213

25137

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=25 \,{\mathrm e}^{2 t} t \\ \end{align*}

0.678

9214

25940

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

0.678

9215

6701

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

0.679

9216

9780

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

0.679

9217

15442

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=\sin \left (x \right ) \\ \end{align*}

0.679

9218

19029

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

0.679

9219

19032

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

0.679

9220

20212

\begin{align*} x^{\prime }+4 x+3 y&=t \\ y^{\prime }+2 x+5 y&={\mathrm e}^{t} \\ \end{align*}

0.679

9221

20425

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

0.679

9222

22747

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

0.679

9223

2060

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

Series expansion around \(x=0\).

0.680

9224

2219

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=30 \cos \left (x \right )-10 \sin \left (x \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -4 \\ y^{\prime \prime }\left (0\right ) &= 16 \\ \end{align*}

0.680

9225

2427

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

Series expansion around \(t=0\).

0.680

9226

7305

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

0.680

9227

12506

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

0.680

9228

14321

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

0.680

9229

15443

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

0.680

9230

15451

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

0.680

9231

15688

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \\ \end{align*}

0.680

9232

917

\begin{align*} x^{\prime \prime }+4 x^{\prime }+5 x&=10 \cos \left (3 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.681

9233

1811

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

0.681

9234

1845

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

Series expansion around \(x=2\).

0.681

9235

2034

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

Series expansion around \(x=0\).

0.681

9236

2057

\begin{align*} 16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.681

9237

3142

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-3 y&=\sin \left (x \right )-8 x \\ y \left (0\right ) &= {\frac {1}{2}} \\ y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

0.681

9238

4087

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

0.681

9239

5797

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

0.681

9240

6938

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

0.681

9241

7654

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

Series expansion around \(t=0\).

0.681

9242

8075

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

Series expansion around \(x=0\).

0.681

9243

9272

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

0.681

9244

9489

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

Series expansion around \(x=1\).

0.681

9245

9515

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

Series expansion around \(x=0\).

0.681

9246

10558

\begin{align*} x^{2} \left (x +2\right ) y^{\prime \prime }+5 x \left (1-x \right ) y^{\prime }-\left (2-8 x \right ) y&=0 \\ \end{align*}

0.681

9247

19519

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

0.681

9248

24899

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

0.681

9249

25123

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=25 \,{\mathrm e}^{2 t} t \\ \end{align*}

0.681

9250

27374

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

0.681

9251

27563

\begin{align*} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.681

9252

2605

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

0.682

9253

7639

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

Series expansion around \(x=1\).

0.682

9254

14917

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

0.682

9255

18160

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

0.682

9256

19156

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

0.682

9257

19167

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

0.682

9258

23746

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

Series expansion around \(x=0\).

0.682

9259

26560

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

0.682

9260

3724

\begin{align*} y^{\prime \prime }-y&=9 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.683

9261

3745

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

0.683

9262

9983

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

With initial conditions

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

0.683

9263

9996

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

0.683

9264

12284

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

0.683

9265

16949

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

0.683

9266

19521

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

0.683

9267

920

\begin{align*} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \\ x \left (0\right ) &= 10 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.684

9268

3845

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

0.684

9269

3910

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

0.684

9270

4469

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

0.684

9271

15446

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

With initial conditions

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

0.684

9272

17030

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

0.684

9273

17450

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&=-648 t^{2} {\mathrm e}^{5 t} \\ \end{align*}

0.684

9274

17500

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

0.684

9275

17684

\begin{align*} y^{\prime \prime }-11 y^{\prime }+30 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.684

9276

18262

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

0.684

9277

19701

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

0.684

9278

21304

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

0.684

9279

23747

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

Series expansion around \(x=0\).

0.684

9280

24661

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

0.684

9281

24753

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

0.684

9282

27133

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

N/A

N/A

N/A

0.684

9283

4460

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

0.685

9284

6866

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

0.685

9285

8035

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

0.685

9286

8812

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=50 \,{\mathrm e}^{2 x} \\ \end{align*}

0.685

9287

9695

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

0.685

9288

9777

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

0.685

9289

10403

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

0.685

9290

16407

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

0.685

9291

21971

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

0.685

9292

23726

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

Series expansion around \(x=0\).

0.685

9293

23927

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

0.685

9294

24732

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

0.685

9295

25759

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

0.685

9296

2595

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

0.686

9297

3275

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

0.686

9298

12894

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

0.686

9299

13071

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

0.686

9300

27033

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

Using Laplace transform method.

0.686