2.3.138 Problems 13701 to 13800

Table 2.819: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13701

11890

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

1.312

13702

12695

\begin{align*} y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}-\frac {\left (-17 \sin \left (x \right )^{2}-1\right ) y}{4 \sin \left (x \right )^{2}} \\ \end{align*}

1.312

13703

12906

\begin{align*} 24+12 y x +x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\ \end{align*}

1.312

13704

13717

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

1.312

13705

14785

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

1.312

13706

16491

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

1.312

13707

17478

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

1.312

13708

1187

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

1.313

13709

2341

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

1.313

13710

12315

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

1.313

13711

14624

\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \\ \end{align*}

1.313

13712

24928

\begin{align*} y^{\prime }&=3 y+12 \\ y \left (0\right ) &= -2 \\ \end{align*}

1.313

13713

1102

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

1.314

13714

6177

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

1.314

13715

9098

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

1.314

13716

12488

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

1.315

13717

14843

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

1.315

13718

7084

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

1.316

13719

11749

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

1.316

13720

12868

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

1.316

13721

23631

\begin{align*} y^{\prime \prime }+4 y&=4 \cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}
Using Laplace transform method.

1.316

13722

12541

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

1.317

13723

17718

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

1.317

13724

23721

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

1.317

13725

103

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

1.318

13726

9864

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

1.318

13727

14989

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

1.318

13728

5631

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

1.319

13729

17352

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

1.319

13730

667

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

1.320

13731

10228

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

1.320

13732

21875

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

1.320

13733

22310

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

1.320

13734

24351

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

1.320

13735

12587

\begin{align*} y^{\prime \prime }&=\frac {\left (5 x -4\right ) y^{\prime }}{x \left (x -1\right )}-\frac {\left (9 x -6\right ) y}{x^{2} \left (x -1\right )} \\ \end{align*}

1.321

13736

14070

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

1.321

13737

15020

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

1.321

13738

1549

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

1.322

13739

2608

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

1.322

13740

3957

\begin{align*} -y+y^{\prime }&=4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.322

13741

9341

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

1.322

13742

5579

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

1.323

13743

8224

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

1.323

13744

10181

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

1.323

13745

19986

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

1.323

13746

21459

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

1.323

13747

23050

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

1.323

13748

2635

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

1.325

13749

3271

\begin{align*} y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\ y \left (0\right ) &= \frac {\pi }{4} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.325

13750

10260

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

1.325

13751

20375

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

1.325

13752

23615

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

1.325

13753

23657

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=3 t^{3}-9 t^{2}-5 t +1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}
Using Laplace transform method.

1.325

13754

293

\begin{align*} y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.326

13755

10178

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

1.326

13756

16483

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

1.326

13757

23616

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

1.326

13758

8154

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

1.327

13759

17531

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

1.327

13760

25582

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

1.327

13761

9917

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

1.328

13762

14306

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

1.328

13763

10085

\begin{align*} y^{\prime \prime }-y^{\prime } x -y x -x^{5}+24&=0 \\ \end{align*}

1.329

13764

18810

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ y \left (-1\right ) &= 2 \\ y^{\prime }\left (-1\right ) &= 3 \\ \end{align*}

1.329

13765

1513

\begin{align*} y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.330

13766

13774

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

1.330

13767

18931

\begin{align*} y^{\prime \prime }+4 y&=\operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}
Using Laplace transform method.

1.330

13768

22743

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

1.330

13769

25527

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

1.330

13770

23744

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

1.331

13771

5722

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

1.332

13772

12595

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

1.332

13773

14728

\begin{align*} y^{\prime \prime }+8 y^{\prime } x -4 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.332

13774

15230

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.332

13775

20198

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

1.332

13776

21035

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

1.332

13777

21609

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

1.332

13778

22856

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

1.332

13779

23103

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

1.332

13780

12838

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

1.333

13781

16745

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

1.333

13782

22302

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

1.333

13783

3574

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

1.335

13784

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*}

1.335

13785

11447

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

1.335

13786

15501

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

1.335

13787

16812

\begin{align*} y^{\prime \prime }-16 y&=\delta \left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.335

13788

17279

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

1.335

13789

5990

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

1.336

13790

6379

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

1.336

13791

8335

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

1.336

13792

11419

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

1.336

13793

20371

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

1.336

13794

259

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

1.337

13795

22284

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

1.337

13796

7207

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

1.338

13797

17101

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

1.339

13798

17444

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=52 \sin \left (3 t \right ) \\ \end{align*}

1.339

13799

19482

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

1.339

13800

23366

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

1.339