2.3.147 Problems 14601 to 14700

Table 2.843: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14601

14662

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=x \,{\mathrm e}^{-3 x} \sin \left (2 x \right )+x^{2} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \\ \end{align*}

1.707

14602

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*}

1.707

14603

9770

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

1.708

14604

18286

\begin{align*} y^{\prime \prime }-y^{\prime }-5 y&=1 \\ y \left (\infty \right ) &= -{\frac {1}{5}} \\ \end{align*}

1.708

14605

24718

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

1.708

14606

6137

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

1.709

14607

18871

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

1.710

14608

24039

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

1.710

14609

16999

\begin{align*} t^{2} y^{\prime \prime }-12 y^{\prime } t +42 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}

1.711

14610

2064

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.712

14611

9494

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

1.713

14612

22528

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

1.713

14613

15162

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

1.714

14614

15502

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

1.714

14615

19095

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

1.715

14616

2475

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

1.716

14617

6529

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

1.716

14618

13695

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

1.716

14619

8976

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

1.717

14620

13742

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

1.717

14621

20802

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

1.717

14622

24846

\begin{align*} 9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\ \end{align*}

1.717

14623

22653

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

1.718

14624

11447

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

1.719

14625

11861

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

1.719

14626

16555

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

1.719

14627

14489

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

1.720

14628

17525

\begin{align*} y^{\prime \prime }+9 y&=\csc \left (3 t \right ) \\ y \left (\frac {\pi }{12}\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{12}\right ) &= 1 \\ \end{align*}

1.720

14629

18207

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

1.720

14630

24798

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

1.720

14631

15166

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

1.721

14632

26470

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

1.721

14633

17381

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

1.722

14634

24934

\begin{align*} y^{\prime \prime }&=6 \sin \left (3 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

1.722

14635

5056

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

1.723

14636

12416

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

1.723

14637

20804

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

1.723

14638

8000

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

1.724

14639

20541

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

1.724

14640

8457

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

1.725

14641

11604

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

1.725

14642

6508

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

1.726

14643

6955

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

1.726

14644

22552

\begin{align*} i^{\prime }+i&={\mathrm e}^{t} \\ \end{align*}

1.726

14645

9240

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

1.727

14646

12951

\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}-4 y^{2}&=0 \\ \end{align*}

1.727

14647

16474

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

1.727

14648

19003

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

1.727

14649

21381

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

1.727

14650

22967

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

1.727

14651

24488

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

1.727

14652

86

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

1.728

14653

21896

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

1.729

14654

21987

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

1.729

14655

26344

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

1.729

14656

167

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

1.730

14657

1819

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

1.730

14658

9415

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

1.730

14659

12419

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

1.730

14660

17782

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

1.730

14661

20033

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\ \end{align*}

1.730

14662

22226

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

1.730

14663

23510

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

1.730

14664

2839

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

1.731

14665

8354

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

1.731

14666

8747

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

1.731

14667

16305

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

1.731

14668

16518

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.731

14669

9145

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

1.733

14670

23326

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

1.733

14671

26348

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

1.733

14672

5397

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

1.734

14673

19983

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

1.734

14674

25692

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

1.734

14675

17623

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

1.735

14676

17990

\begin{align*} 4 {y^{\prime }}^{2}-9 x&=0 \\ \end{align*}

1.735

14677

25682

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \\ \end{align*}

1.735

14678

15403

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

1.736

14679

13755

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

1.737

14680

13825

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

1.737

14681

14249

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

1.737

14682

15411

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

1.737

14683

19926

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

1.737

14684

25476

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

1.737

14685

1745

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

1.738

14686

8111

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

1.738

14687

26186

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

1.738

14688

8078

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

1.739

14689

18958

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=g \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

1.739

14690

8086

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

1.740

14691

11710

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

1.740

14692

14324

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

1.740

14693

16470

\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 12 \\ \end{align*}

1.740

14694

25279

\begin{align*} t y^{\prime \prime }-y^{\prime }+4 y t^{3}&=4 t^{5} \\ \end{align*}

1.740

14695

87

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

1.741

14696

9635

\begin{align*} y^{\prime \prime }+16 y&=\left \{\begin {array}{cc} \cos \left (4 t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.741

14697

12494

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

1.741

14698

2363

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

1.742

14699

8390

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

1.742

14700

11683

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

1.743