2.3.148 Problems 14701 to 14800

Table 2.869: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14701

9761

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

1.641

14702

15434

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=2-6 x \\ \end{align*}

1.641

14703

13392

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

1.642

14704

23371

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

1.642

14705

26001

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

Using Laplace transform method.

1.642

14706

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*}

1.643

14707

21124

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

1.644

14708

25284

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

Using Laplace transform method.

1.644

14709

2430

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

1.645

14710

6522

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

1.645

14711

7325

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

1.645

14712

8321

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

1.645

14713

17302

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

1.645

14714

22850

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

Series expansion around \(x=0\).

1.645

14715

27027

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

Using Laplace transform method.

1.645

14716

3220

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

1.647

14717

26590

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=\left (12 x -7\right ) {\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.647

14718

27087

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

1.647

14719

2361

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

1.648

14720

9865

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

Series expansion around \(x=0\).

1.648

14721

16274

\begin{align*} x y^{\prime }+\left (2+5 x \right ) y&=\frac {20}{x} \\ \end{align*}

1.648

14722

18309

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

1.648

14723

19785

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

1.648

14724

22855

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

Series expansion around \(x=0\).

1.648

14725

22872

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

Series expansion around \(x=0\).

1.648

14726

9637

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

1.649

14727

8041

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

1.650

14728

13707

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

1.650

14729

18795

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

1.650

14730

22881

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

Series expansion around \(x=0\).

1.650

14731

6536

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

1.651

14732

18267

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

1.651

14733

12941

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

1.652

14734

27267

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

1.652

14735

27363

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

1.652

14736

12913

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

1.653

14737

9954

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

Series expansion around \(x=0\).

1.654

14738

14149

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

1.654

14739

15527

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

1.654

14740

8154

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

1.655

14741

26635

\begin{align*} \left (4 x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x -1\right ) y^{\prime }-4 y&=12 x^{2}-6 x \\ \end{align*}

1.655

14742

9908

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

Series expansion around \(x=0\).

1.656

14743

15068

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

1.656

14744

18872

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

1.656

14745

710

\begin{align*} 2 x y^{\prime }+y&=10 \sqrt {x} \\ \end{align*}

1.657

14746

24876

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

1.657

14747

5442

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

1.658

14748

5681

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

1.658

14749

9186

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

1.658

14750

9914

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

Series expansion around \(x=0\).

1.658

14751

15679

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

1.658

14752

17637

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

1.658

14753

19791

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

1.658

14754

21331

\begin{align*} y^{\prime }&=6 y \\ \end{align*}

1.658

14755

23155

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

1.658

14756

20074

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

1.659

14757

2399

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

1.660

14758

17452

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

1.660

14759

1332

\begin{align*} t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y&=0 \\ \end{align*}

1.661

14760

15174

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

1.661

14761

20126

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

1.661

14762

20411

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

1.661

14763

20503

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

1.661

14764

25758

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

1.661

14765

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*}

1.662

14766

20424

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

1.662

14767

13351

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

1.663

14768

22307

\begin{align*} s^{\prime }&=9 \sqrt {u} \\ s \left (4\right ) &= 16 \\ \end{align*}

1.663

14769

5953

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

1.664

14770

14067

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

1.664

14771

27381

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

1.664

14772

9034

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

1.665

14773

9953

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

Series expansion around \(x=0\).

1.665

14774

2707

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

With initial conditions

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

1.667

14775

5840

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

1.667

14776

6034

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

1.667

14777

8755

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

1.667

14778

17662

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

1.667

14779

1185

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

1.668

14780

16155

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

1.668

14781

3227

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

1.669

14782

13055

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

1.669

14783

14758

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

Series expansion around \(x=0\).

1.669

14784

16232

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

1.670

14785

24411

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

1.670

14786

2757

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

1.671

14787

5849

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

1.671

14788

6201

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

1.671

14789

9916

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

Series expansion around \(x=0\).

1.671

14790

18111

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

1.671

14791

19864

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

1.671

14792

21335

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

1.671

14793

2384

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

1.672

14794

6854

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

1.672

14795

22870

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

Series expansion around \(x=0\).

1.672

14796

9942

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

Series expansion around \(x=0\).

1.673

14797

218

\begin{align*} y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= -10 \\ \end{align*}

1.674

14798

7643

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

Series expansion around \(x=1\).

1.674

14799

8988

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

Series expansion around \(x=-2\).

1.674

14800

16160

\begin{align*} y^{\prime \prime }+3 y^{\prime }+8 y&={\mathrm e}^{-x^{2}} \\ \end{align*}

1.674