2.3.174 Problems 17301 to 17400

Table 2.921: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

17301

22805

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

2.747

17302

24519

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

2.747

17303

25776

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

2.747

17304

125

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

2.748

17305

25021

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

2.748

17306

3058

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

2.749

17307

19251

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

2.749

17308

27135

\(\left [\begin {array}{ccc} 3 & 2 & 0 \\ 2 & 0 & i \\ 0 & -i & 0 \end {array}\right ]\)

N/A

N/A

N/A

2.749

17309

4996

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

2.750

17310

7011

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

2.750

17311

13296

\begin{align*} y^{\prime }&=a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{s x}+d \,{\mathrm e}^{-k x} \\ \end{align*}

2.750

17312

496

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

Series expansion around \(x=0\).

2.751

17313

18291

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

2.751

17314

6852

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

2.753

17315

6042

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

2.754

17316

17655

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

2.754

17317

16599

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

2.755

17318

17182

\begin{align*} 3 y+y^{\prime }&=27 t^{2}+9 \\ \end{align*}

2.755

17319

691

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

2.756

17320

7004

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

2.756

17321

20543

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

2.756

17322

1000

\begin{align*} x_{1}^{\prime }&=23 x_{1}-18 x_{2}-16 x_{3} \\ x_{2}^{\prime }&=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\ x_{3}^{\prime }&=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\ x_{4}^{\prime }&=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \\ \end{align*}

2.757

17323

19089

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

2.757

17324

24982

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

2.758

17325

4699

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

2.759

17326

14539

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

2.759

17327

14912

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

2.759

17328

29

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

2.760

17329

20824

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

2.760

17330

14372

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

Using Laplace transform method.

2.761

17331

24520

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

2.763

17332

4766

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

2.764

17333

8774

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

2.765

17334

17189

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

2.765

17335

1167

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

2.766

17336

8682

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

2.766

17337

17646

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

2.766

17338

1242

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

2.767

17339

1564

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

2.767

17340

15776

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

2.767

17341

20694

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

2.767

17342

3019

\begin{align*} r^{\prime }&=r \cot \left (\theta \right ) \\ \end{align*}

2.770

17343

7001

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

2.770

17344

12147

\begin{align*} y^{\prime }&=-\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+x^{2} y^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \\ \end{align*}

2.770

17345

21467

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

2.770

17346

13217

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

2.771

17347

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*}

2.772

17348

17780

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y&=0 \\ \end{align*}

2.772

17349

23194

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

2.772

17350

4611

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

2.773

17351

25807

\begin{align*} y^{\prime }&=10+3 y-y^{2} \\ \end{align*}

2.773

17352

27740

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

2.773

17353

1169

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

2.774

17354

12703

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

2.774

17355

26267

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

2.775

17356

6348

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

2.776

17357

7342

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

2.777

17358

25449

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

2.777

17359

727

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

2.778

17360

12948

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

2.778

17361

27279

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

2.778

17362

197

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

2.779

17363

5520

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

2.779

17364

12296

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

2.779

17365

27232

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

2.779

17366

7678

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

2.780

17367

25438

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

2.780

17368

2687

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

Using Laplace transform method.

2.781

17369

9660

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

2.782

17370

21441

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

2.782

17371

1538

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

2.783

17372

5989

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

2.783

17373

11400

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

2.783

17374

25612

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

2.783

17375

88

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

2.785

17376

3028

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

2.786

17377

3257

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

2.786

17378

9224

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

2.786

17379

9797

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

2.786

17380

12026

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

2.786

17381

24830

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

2.786

17382

25777

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

2.786

17383

4776

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

2.787

17384

6378

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

2.787

17385

23338

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

2.787

17386

10250

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

2.788

17387

11690

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

2.788

17388

16345

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

2.788

17389

11318

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

2.789

17390

20741

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

2.789

17391

25700

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

2.789

17392

26753

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

2.790

17393

7155

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

2.793

17394

8432

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

2.793

17395

24930

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

2.793

17396

707

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

2.795

17397

24842

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

2.795

17398

4058

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

Series expansion around \(x=0\).

2.796

17399

6038

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

2.796

17400

6417

\begin{align*} f \left (x \right )^{2} y^{\prime \prime }&=-24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime } \\ \end{align*}

2.796