2.3.115 Problems 11401 to 11500

Table 2.773: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11401

19501

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=12 x -10 \\ \end{align*}

0.849

11402

19601

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

0.849

11403

20919

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.849

11404

7674

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

0.850

11405

9334

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

0.850

11406

9428

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

0.850

11407

14049

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

0.850

11408

14128

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

0.850

11409

14942

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

0.850

11410

16900

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

0.850

11411

19031

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

0.850

11412

20527

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

0.850

11413

21167

\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*}

0.850

11414

21672

\begin{align*} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.850

11415

23810

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

0.850

11416

25346

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

0.850

11417

2698

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

0.851

11418

12605

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

0.851

11419

21038

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

0.851

11420

21691

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

0.851

11421

21776

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

0.851

11422

23564

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

0.851

11423

23795

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}

0.851

11424

646

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{3} \\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 17 \\ \end{align*}

0.852

11425

2446

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

0.852

11426

3755

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

0.852

11427

3902

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

0.852

11428

6249

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

0.852

11429

9533

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

0.852

11430

12900

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

0.852

11431

14607

\begin{align*} y^{\prime \prime }+6 y^{\prime }+58 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.852

11432

14875

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

0.852

11433

17787

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

0.852

11434

1970

\begin{align*} x^{2} \left (6+x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }+\left (2 x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.853

11435

10482

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

0.853

11436

15772

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

0.853

11437

17687

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

0.853

11438

21258

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

0.853

11439

22918

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

0.853

11440

1191

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

0.854

11441

9518

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

0.854

11442

15066

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

0.854

11443

16889

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

0.854

11444

17684

\begin{align*} y^{\prime \prime }-11 y^{\prime }+30 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.854

11445

25576

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

0.854

11446

1966

\begin{align*} x^{2} \left (8+x \right ) y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.855

11447

9001

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +\left (-x^{3}+3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.855

11448

14672

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

0.855

11449

14936

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

0.855

11450

19039

\begin{align*} x_{1}^{\prime }&=-k_{1} x_{1} \\ x_{2}^{\prime }&=k_{1} x_{1}-k_{2} x_{2} \\ x_{3}^{\prime }&=k_{2} x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= m_{0} \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

0.855

11451

22901

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

0.855

11452

23443

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

0.855

11453

1943

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

0.856

11454

3400

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

0.856

11455

3889

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

0.856

11456

4684

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

0.856

11457

8227

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

0.856

11458

10225

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

0.856

11459

14083

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

0.856

11460

15975

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

0.856

11461

20571

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

0.856

11462

23437

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

0.856

11463

23717

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

0.856

11464

814

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

0.857

11465

17899

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

0.857

11466

19875

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

0.857

11467

21921

\begin{align*} 4 y+y^{\prime \prime }&=x \sin \left (x \right ) \\ y \left (0\right ) &= {\frac {7}{9}} \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{6}-1 \\ \end{align*}

0.857

11468

23556

\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }&=-2 x_{1}+3 x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 3 \\ \end{align*}

0.857

11469

23834

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

0.857

11470

22

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

0.858

11471

2649

\begin{align*} t^{2} y^{\prime \prime }-y^{\prime } t -\left (t^{2}+\frac {5}{4}\right ) y&=0 \\ \end{align*}
Series expansion around \(t=0\).

0.858

11472

14355

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

0.858

11473

15502

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}

0.858

11474

19454

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

0.858

11475

22923

\begin{align*} x^{\prime }+2 y&=4 \,{\mathrm e}^{2 t} \\ x+y^{\prime }-y&=2 \,{\mathrm e}^{2 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 7 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.858

11476

1969

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

0.859

11477

2009

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+14 x +5\right ) y^{\prime }+\left (12 x^{2}+18 x +4\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.859

11478

2024

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (5+9 x \right ) y^{\prime }+\left (3 x +4\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.859

11479

14398

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

0.859

11480

21904

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

0.859

11481

23517

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

0.859

11482

9795

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

0.860

11483

15716

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

0.860

11484

19219

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

0.860

11485

9733

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

0.861

11486

9749

\begin{align*} x^{6} {y^{\prime }}^{3}-3 y^{\prime } x -3 y&=0 \\ \end{align*}

0.861

11487

14803

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.861

11488

21611

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

0.861

11489

24535

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

0.861

11490

991

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

0.862

11491

2078

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

0.862

11492

2085

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (6+11 x \right ) y^{\prime }+\left (6+32 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.862

11493

8990

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

0.862

11494

9433

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

0.862

11495

10109

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

0.862

11496

15723

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

0.862

11497

16912

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

0.862

11498

16914

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

0.862

11499

18896

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.862

11500

25349

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

0.862