2.3.186 Problems 18501 to 18600

Table 2.945: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

18501

27278

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

3.320

18502

8664

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

3.321

18503

14894

\begin{align*} x^{\prime }&=\lambda x \\ \end{align*}

3.323

18504

19403

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

3.323

18505

19948

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

3.323

18506

23171

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

3.324

18507

14229

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

3.325

18508

13757

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

3.326

18509

20572

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

3.326

18510

23886

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

3.326

18511

27317

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

3.326

18512

24188

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

3.327

18513

797

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

3.328

18514

26225

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

3.328

18515

14257

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

3.329

18516

16359

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

3.329

18517

17413

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

3.329

18518

25002

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

3.329

18519

3437

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

3.330

18520

10124

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

3.330

18521

19323

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

3.330

18522

26090

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

3.330

18523

1219

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

3.331

18524

16317

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

3.331

18525

3477

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

3.332

18526

4457

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

3.332

18527

16288

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

3.332

18528

24921

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

3.332

18529

12303

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

3.333

18530

20868

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

3.333

18531

3246

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

3.335

18532

2068

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

Series expansion around \(x=0\).

3.336

18533

26696

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

3.336

18534

6317

\begin{align*} y y^{\prime }+y^{\prime \prime }&=-12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right ) \\ \end{align*}

3.338

18535

14042

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

3.338

18536

24114

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-5 x \right ) y^{\prime }+\left (5-6 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

3.338

18537

15534

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

3.339

18538

26092

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

3.339

18539

4674

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

3.340

18540

16343

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

3.341

18541

17960

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

3.341

18542

26357

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

3.341

18543

19713

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

3.343

18544

27261

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

3.343

18545

22330

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

3.346

18546

44

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

3.347

18547

21100

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

3.349

18548

27274

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

3.349

18549

11981

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

3.350

18550

13766

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

3.350

18551

13935

\begin{align*} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y&=0 \\ \end{align*}

3.351

18552

202

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

3.352

18553

3536

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

3.352

18554

8468

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

3.353

18555

8654

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\delta \left (t -\frac {\pi }{2}\right )+\cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

3.353

18556

19806

\begin{align*} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

3.353

18557

8982

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

3.355

18558

15961

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

3.355

18559

24196

\begin{align*} \left (6+3 y x -4 y^{3}\right ) x +\left (x^{3}-6 x^{2} y^{2}-1\right ) y^{\prime }&=0 \\ \end{align*}

3.355

18560

3516

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

3.357

18561

14849

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

3.357

18562

25312

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

Using Laplace transform method.

3.358

18563

8241

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

3.359

18564

8881

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

3.360

18565

19078

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

3.360

18566

8736

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

3.361

18567

4095

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

3.362

18568

4834

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

3.362

18569

2510

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

3.363

18570

5619

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

3.364

18571

6449

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

3.364

18572

2075

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 y x&=0 \\ \end{align*}

Series expansion around \(x=0\).

3.365

18573

12876

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

3.366

18574

4270

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

3.368

18575

23895

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

3.368

18576

686

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

3.369

18577

6955

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

3.369

18578

11899

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

3.369

18579

1848

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

Series expansion around \(x=0\).

3.370

18580

2070

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

3.370

18581

2326

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

3.371

18582

13227

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

3.371

18583

22080

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

3.371

18584

3594

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

3.372

18585

5878

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

3.373

18586

7563

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

3.373

18587

9088

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

3.373

18588

27421

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

3.373

18589

11376

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

3.374

18590

2074

\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

3.375

18591

25574

\begin{align*} 4 a y^{\prime \prime }+b y^{\prime }+\frac {c y}{4}&=f \left (t \right ) \\ \end{align*}

3.375

18592

1849

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-\left (6 x +4\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

3.376

18593

7161

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

3.376

18594

14487

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

3.377

18595

7021

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

3.378

18596

14846

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

3.378

18597

4193

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

3.380

18598

18536

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

3.380

18599

11406

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

3.381

18600

11883

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

3.381