2.3.118 Problems 11701 to 11800

Table 2.809: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11701

14644

\begin{align*} y^{\prime \prime }-8 y^{\prime }+15 y&=9 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 10 \\ \end{align*}

0.940

11702

14873

\begin{align*} u^{\prime }&=4 t \ln \left (t \right ) \\ \end{align*}

0.940

11703

16736

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

0.940

11704

18450

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

With initial conditions

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

0.940

11705

25784

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

0.940

11706

26584

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

0.940

11707

6931

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

0.941

11708

7296

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

0.941

11709

14049

\begin{align*} {y^{\prime }}^{3}-\left (y^{2}+2 x \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*}

0.941

11710

14556

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

0.941

11711

15277

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

0.941

11712

16744

\begin{align*} y^{\prime \prime }+36 y&=6 \sec \left (6 x \right ) \\ \end{align*}

0.941

11713

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*}

0.941

11714

23598

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

With initial conditions

\begin{align*} x \left (0\right ) &= b \\ y \left (0\right ) &= \frac {d b}{a +d} \\ \end{align*}

0.941

11715

25359

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

0.941

11716

5638

\begin{align*} {y^{\prime }}^{3}-\left (y^{2}+2 x \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*}

0.942

11717

8527

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

Series expansion around \(x=0\).

0.942

11718

26657

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

0.942

11719

7343

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

0.943

11720

7727

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

0.943

11721

7911

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

0.943

11722

18442

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

0.943

11723

18856

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{8}+4 y&=3 \cos \left (6 t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.943

11724

20494

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

0.943

11725

620

\begin{align*} x_{1}^{\prime }&=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }&=x_{2} \\ x_{3}^{\prime }&=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }&=-4 x_{2}-x_{4} \\ \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 ) &= 1 \\ \end{align*}

0.944

11726

3163

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

0.944

11727

3504

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

Series expansion around \(z=0\).

0.944

11728

6241

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

0.944

11729

9069

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

0.944

11730

12377

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

0.944

11731

15275

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

0.944

11732

15653

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

0.944

11733

17715

\begin{align*} y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.944

11734

18397

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

0.944

11735

18677

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

0.944

11736

18903

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

Using Laplace transform method.

0.944

11737

19200

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

0.944

11738

20873

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

0.944

11739

21271

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

Series expansion around \(t=0\).

0.944

11740

23102

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

0.944

11741

27385

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

0.944

11742

4538

\begin{align*} y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}&=0 \\ -4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}&=0 \\ -4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}&=0 \\ \end{align*}

0.945

11743

9130

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

0.945

11744

9692

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

0.945

11745

14122

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

0.945

11746

16915

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

Series expansion around \(x=0\).

0.945

11747

23585

\begin{align*} x^{\prime }&=3 x-2 y+2 t^{2} \\ y^{\prime }&=5 x+y-1 \\ \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) &= {\frac {534}{2197}} \\ y \left (0\right ) &= {\frac {567}{2197}} \\ \end{align*}

0.945

11748

2449

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

Series expansion around \(t=0\).

0.946

11749

3349

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

Series expansion around \(x=\frac {\pi }{2}\).

0.947

11750

3771

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

0.947

11751

6402

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

0.947

11752

8084

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

Series expansion around \(x=0\).

0.947

11753

9849

\begin{align*} y^{\prime \prime }+3 x y^{\prime }+7 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.947

11754

10395

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

0.947

11755

16162

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

0.947

11756

19917

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

0.947

11757

22734

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

0.947

11758

4487

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

0.948

11759

5770

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

0.948

11760

12367

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

0.948

11761

21679

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

Series expansion around \(x=0\).

0.948

11762

26618

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

0.948

11763

27726

\begin{align*} \left (3 x^{3}+x \right ) y^{\prime \prime }+2 y^{\prime }-6 y x&=-12 x^{2}+4 \\ \end{align*}

0.948

11764

3354

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

Series expansion around \(x=0\).

0.949

11765

4539

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

0.949

11766

14382

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

0.949

11767

14622

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

0.949

11768

14806

\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\)

N/A

N/A

N/A

0.949

11769

15467

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

0.949

11770

21661

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

Series expansion around \(x=0\).

0.949

11771

24669

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

0.949

11772

1451

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

0.950

11773

9851

\begin{align*} \left (x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }-9 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.950

11774

10261

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

0.950

11775

14740

\begin{align*} \left (2 x^{2}-3\right ) y^{\prime \prime }-2 x y^{\prime }+y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

Series expansion around \(x=0\).

0.950

11776

20471

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

0.950

11777

2025

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

Series expansion around \(x=0\).

0.951

11778

14802

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\)

N/A

N/A

N/A

0.951

11779

18273

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=16 \,{\mathrm e}^{-x}+9 x -6 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.951

11780

22814

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -3 \\ \end{align*}

Using Laplace transform method.

0.951

11781

24852

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

0.951

11782

4020

\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (7+3 x \right ) y^{\prime }+\left (1+6 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.952

11783

5577

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

0.952

11784

600

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

0.953

11785

7653

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

Series expansion around \(x=0\).

0.953

11786

18350

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

0.953

11787

18891

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

Using Laplace transform method.

0.953

11788

19421

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

0.953

11789

27649

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

0.953

11790

464

\begin{align*} \left (2 x^{3}+6 x^{2}\right ) y^{\prime \prime }+21 x y^{\prime }+9 \left (x^{2}-1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.954

11791

891

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

0.954

11792

1948

\begin{align*} 12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.954

11793

2643

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

Series expansion around \(t=0\).

0.954

11794

6437

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

0.954

11795

8111

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

Series expansion around \(x=0\).

0.954

11796

10394

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

0.954

11797

12996

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

0.954

11798

13899

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

0.954

11799

15047

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

0.954

11800

16050

\begin{align*} x^{\prime }&=-10 x+10 y \\ y^{\prime }&=28 x-y \\ z^{\prime }&=-\frac {8 z}{3} \\ \end{align*}

0.954