2.3.116 Problems 11501 to 11600

Table 2.805: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11501

12401

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

1.750

11502

12428

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

1.750

11503

12445

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

1.750

11504

23639

\begin{align*} y^{\prime \prime \prime }-27 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 6 \\ y^{\prime \prime }\left (0\right ) &= 18 \\ \end{align*}

Using Laplace transform method.

1.750

11505

17469

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

1.752

11506

4611

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

1.753

11507

9335

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

1.753

11508

13921

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

1.753

11509

18230

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

1.753

11510

18739

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

1.753

11511

19596

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

Series expansion around \(x=0\).

1.753

11512

20560

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

1.753

11513

21032

\begin{align*} {\mathrm e}^{x^{\prime }}&=x \\ x \left (t_{0} \right ) &= a \\ \end{align*}

1.753

11514

25135

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=6 \,{\mathrm e}^{-4 t} \\ \end{align*}

1.753

11515

10358

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

Series expansion around \(x=0\).

1.754

11516

15279

\begin{align*} x^{\prime }&=-4 x+9 y+12 \,{\mathrm e}^{-t} \\ y^{\prime }&=-5 x+2 y \\ \end{align*}

1.754

11517

17193

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

1.754

11518

18998

\begin{align*} x_{1}^{\prime }&=x_{1}+5 x_{2}+3 x_{3}-5 x_{4} \\ x_{2}^{\prime }&=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4} \\ x_{3}^{\prime }&=-x_{2}-2 x_{3}+x_{4} \\ x_{4}^{\prime }&=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4} \\ \end{align*}

1.754

11519

22230

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

Using Laplace transform method.

1.754

11520

27158

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

1.754

11521

6519

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

1.755

11522

25133

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{-2 t} \\ \end{align*}

1.755

11523

9514

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

Series expansion around \(x=0\).

1.756

11524

15772

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

1.756

11525

7173

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

Series expansion around \(x=0\).

1.757

11526

14753

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

Series expansion around \(x=0\).

1.757

11527

16472

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

1.757

11528

23594

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

1.757

11529

6141

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

1.758

11530

23562

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

1.758

11531

26943

\begin{align*} y^{\prime \prime }-14 y^{\prime }+49 y&=0 \\ \end{align*}

1.758

11532

5550

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

1.759

11533

20525

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

1.759

11534

22941

\begin{align*} x^{\prime }+3 x+4 y&=8 \,{\mathrm e}^{t} \\ -x+y^{\prime }-y&=0 \\ \end{align*}

1.759

11535

25936

\begin{align*} y^{\prime \prime }-4 y&=8 x^{2} \\ \end{align*}

1.759

11536

8807

\begin{align*} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t}&=0 \\ \end{align*}

1.762

11537

19603

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

Series expansion around \(x=0\).

1.762

11538

20522

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

1.762

11539

24605

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

1.762

11540

1741

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

1.763

11541

2482

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

1.763

11542

2746

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 0 \\ \end{align*}

1.763

11543

6411

\begin{align*} 24-48 y x +\left (-12 x^{2}+1\right ) \left (y^{2}+3 y^{\prime }\right )+2 x \left (-4 x^{2}+1\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )&=0 \\ \end{align*}

1.763

11544

9379

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

Series expansion around \(x=0\).

1.763

11545

18322

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

1.763

11546

10011

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

1.764

11547

17171

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

1.764

11548

23582

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -{\frac {1}{2}} \\ x_{2} \left (0\right ) &= -{\frac {1}{4}} \\ \end{align*}

1.764

11549

25374

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

With initial conditions

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

1.764

11550

5557

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

1.765

11551

17419

\begin{align*} y^{\prime \prime }-16 y&=0 \\ \end{align*}

1.765

11552

5401

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

1.766

11553

8810

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

1.766

11554

13791

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

1.766

11555

19604

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

Series expansion around \(x=0\).

1.766

11556

20149

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

Series expansion around \(x=0\).

1.766

11557

11821

\begin{align*} 8 {y^{\prime }}^{3} x -12 y {y^{\prime }}^{2}+9 y&=0 \\ \end{align*}

1.767

11558

16586

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

1.767

11559

5444

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

1.768

11560

6068

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

1.768

11561

9693

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

1.768

11562

17780

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

1.768

11563

199

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

1.769

11564

5603

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

1.769

11565

9783

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

1.769

11566

17362

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

1.769

11567

23578

\begin{align*} N_{1}^{\prime }&=4 N_{1}-6 N_{2} \\ N_{2}^{\prime }&=8 N_{1}-10 N_{2} \\ \end{align*}

With initial conditions

\begin{align*} N_{1} \left (0\right ) &= 100000 \\ N_{2} \left (0\right ) &= 1000 \\ \end{align*}

1.769

11568

7622

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

Series expansion around \(x=0\).

1.770

11569

22901

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

1.770

11570

24598

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

1.770

11571

16040

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

1.771

11572

16688

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

1.771

11573

16701

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

1.771

11574

25131

\begin{align*} y^{\prime \prime }-4 y&={\mathrm e}^{-6 t} \\ \end{align*}

1.771

11575

9853

\begin{align*} \left (9 x^{2}+1\right ) y^{\prime \prime }-18 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.772

11576

25939

\begin{align*} y^{\prime \prime }-y&=5 \,{\mathrm e}^{x} \\ \end{align*}

1.772

11577

1614

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

1.773

11578

5445

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

1.773

11579

6952

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

1.773

11580

9632

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

Using Laplace transform method.

1.773

11581

13943

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

1.773

11582

16834

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

Series expansion around \(x=0\).

1.773

11583

17529

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y&=2 \ln \left (t \right ) \\ \end{align*}

1.773

11584

17873

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

1.773

11585

19858

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

1.773

11586

24614

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

1.773

11587

27090

\(\left [\begin {array}{cc} -5 & 0 \\ 1 & 2 \end {array}\right ]\)

N/A

N/A

N/A

1.773

11588

6864

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

1.774

11589

11749

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

1.775

11590

20551

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

1.775

11591

12346

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

1.776

11592

27089

\(\left [\begin {array}{cc} -2 & 0 \\ 1 & 4 \end {array}\right ]\)

N/A

N/A

N/A

1.776

11593

27784

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

Series expansion around \(x=0\).

1.776

11594

6168

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

1.777

11595

11449

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

1.777

11596

14729

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

Series expansion around \(x=0\).

1.777

11597

15089

\begin{align*} x^{\prime \prime }+9 x&=t \sin \left (3 t \right ) \\ \end{align*}

1.777

11598

16759

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

Using Laplace transform method.

1.777

11599

24604

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

1.777

11600

14944

\begin{align*} x^{\prime \prime }+4 x&=289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \\ \end{align*}

1.778