2.3.228 Problems 22701 to 22800

Table 2.1029: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22701

7515

\begin{align*} r^{\prime }&=r^{2}+\frac {2 r}{t} \\ \end{align*}

7.793

22702

4355

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

7.795

22703

13678

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

7.795

22704

7250

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

7.796

22705

12274

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

7.796

22706

738

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

7.797

22707

2537

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

7.798

22708

3020

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

7.800

22709

7469

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

7.800

22710

13368

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

7.800

22711

12224

\begin{align*} y^{\prime }&=\frac {-32 a x y-8 a^{2} x^{3}-16 a b \,x^{2}-32 a x +64 y^{3}+48 a \,x^{2} y^{2}+96 b x y^{2}+12 y a^{2} x^{4}+48 y a \,x^{3} b +48 b^{2} x^{2} y+a^{3} x^{6}+6 a^{2} x^{5} b +12 b^{2} x^{4} a +8 b^{3} x^{3}}{64 y+16 a \,x^{2}+32 b x +64} \\ \end{align*}

7.803

22712

18496

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

7.810

22713

20962

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

7.811

22714

11923

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

7.814

22715

16437

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

7.815

22716

187

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

7.816

22717

4262

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

7.816

22718

22219

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

Series expansion around \(x=0\).

7.816

22719

11652

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

7.821

22720

6291

\begin{align*} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \\ \end{align*}

7.823

22721

21286

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

Using Laplace transform method.

7.824

22722

3481

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

7.826

22723

23854

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

7.827

22724

14763

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

Series expansion around \(x=0\).

7.829

22725

14826

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

Using Laplace transform method.

7.829

22726

8784

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

7.833

22727

5341

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

7.841

22728

11539

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

7.844

22729

12382

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

7.844

22730

8761

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

7.848

22731

7722

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

7.849

22732

6143

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

7.851

22733

14481

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

7.851

22734

13783

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

7.853

22735

22218

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

Series expansion around \(x=0\).

7.856

22736

4863

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

7.857

22737

6476

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

7.858

22738

13878

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

7.861

22739

25664

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

7.861

22740

22993

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

7.862

22741

16313

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

7.864

22742

20780

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

7.864

22743

24193

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

7.867

22744

18488

\begin{align*} r^{\prime }&=\frac {r^{2}}{\theta } \\ r \left (1\right ) &= 2 \\ \end{align*}

7.868

22745

6428

\begin{align*} y y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+{y^{\prime }}^{2} \\ \end{align*}

7.873

22746

12152

\begin{align*} y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \\ \end{align*}

7.878

22747

26260

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

7.879

22748

778

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

7.881

22749

17904

\begin{align*} x^{3} y^{\prime }-\sin \left (y\right )&=1 \\ y \left (\infty \right ) &= 5 \pi \\ \end{align*}

7.881

22750

24961

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

7.888

22751

9123

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

7.890

22752

18567

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

7.890

22753

5752

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

7.891

22754

5965

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

7.893

22755

1675

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

7.895

22756

21797

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

7.895

22757

4962

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

7.896

22758

15511

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

7.897

22759

4424

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

7.898

22760

4303

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

7.901

22761

22606

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

7.901

22762

17268

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

7.910

22763

26380

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

7.911

22764

5903

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

7.912

22765

10126

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

7.912

22766

18594

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

7.912

22767

18922

\begin{align*} y^{\prime \prime }+2 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 1 & \pi \le t \le 2 \pi \\ 0 & t \le 2 \pi \end {array}\right . \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

Using Laplace transform method.

7.913

22768

2508

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

7.917

22769

15037

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

7.918

22770

14162

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

7.919

22771

13314

\begin{align*} x y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{2}+k y+a \,b^{2} x^{2 k} {\mathrm e}^{\lambda x} \\ \end{align*}

7.922

22772

7707

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

7.925

22773

21671

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

Series expansion around \(x=0\).

7.933

22774

7808

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

7.934

22775

22543

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

7.935

22776

22360

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

7.937

22777

5206

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

7.938

22778

11932

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}

7.939

22779

15341

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

7.939

22780

13369

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

7.940

22781

14765

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

Series expansion around \(x=0\).

7.940

22782

753

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

7.941

22783

11954

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

7.942

22784

8665

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

7.943

22785

21089

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

7.944

22786

16377

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

7.948

22787

8279

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

7.951

22788

12055

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

7.951

22789

14494

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

7.953

22790

22576

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

7.954

22791

16436

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

7.955

22792

7701

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

7.957

22793

17333

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

7.957

22794

22575

\begin{align*} i^{\prime }&=\frac {i t^{2}}{t^{3}-i^{3}} \\ \end{align*}

7.957

22795

22598

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

7.961

22796

18576

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

7.967

22797

4712

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

7.970

22798

26254

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

7.970

22799

6986

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

7.971

22800

4971

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

7.974