2.3.149 Problems 14801 to 14900

Table 2.847: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14801

12417

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

1.786

14802

16564

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

1.786

14803

23254

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

1.786

14804

1499

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=t -\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (t -\frac {\pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.787

14805

8861

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

1.787

14806

22767

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

1.787

14807

717

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

1.789

14808

9188

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

1.789

14809

19889

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

1.789

14810

19986

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

1.789

14811

22539

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

1.789

14812

10054

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

1.790

14813

18232

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=18 x -10 \cos \left (x \right ) \\ \end{align*}

1.790

14814

25813

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

1.790

14815

7209

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

1.791

14816

18224

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

1.792

14817

22456

\begin{align*} i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\ i \left (0\right ) &= 0 \\ \end{align*}

1.792

14818

24826

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

1.792

14819

16473

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 4 \\ \end{align*}

1.793

14820

99

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

1.794

14821

2097

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.794

14822

4507

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

1.796

14823

5411

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

1.796

14824

6321

\begin{align*} y^{\prime \prime }&=\operatorname {g3} \left (x \right )+\operatorname {g2} \left (x \right ) y+\operatorname {g1} \left (x \right ) y^{2}+\operatorname {g0} \left (x \right ) y^{3}+\left (\operatorname {f1} \left (x \right )+\operatorname {f0} \left (x \right ) y\right ) y^{\prime } \\ \end{align*}

1.796

14825

12468

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

1.796

14826

15176

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

1.796

14827

609

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

1.797

14828

1235

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

1.797

14829

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*}

1.797

14830

24824

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

1.798

14831

63

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

1.799

14832

9385

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

1.799

14833

13055

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

1.799

14834

18322

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

1.799

14835

19271

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

1.799

14836

24827

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

1.799

14837

5883

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

1.800

14838

15282

\begin{align*} x^{\prime }&=-14 x+39 y+78 \sinh \left (t \right ) \\ y^{\prime }&=-6 x+16 y+6 \cosh \left (t \right ) \\ \end{align*}

1.800

14839

5400

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

1.801

14840

8110

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

1.801

14841

20204

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

1.801

14842

5758

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

1.802

14843

16697

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

1.802

14844

11425

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

1.803

14845

15133

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

1.803

14846

16571

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

1.803

14847

23138

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

1.803

14848

12469

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

1.804

14849

4376

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

1.805

14850

11428

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

1.805

14851

14217

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

1.805

14852

6202

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

1.806

14853

13898

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

1.806

14854

16237

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

1.806

14855

17158

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

1.806

14856

22634

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

1.807

14857

17132

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

1.809

14858

23466

\begin{align*} 3 x^{2} y^{\prime \prime }-2 y^{\prime } x -8 y&=3 x +5 \\ \end{align*}

1.809

14859

8283

\begin{align*} y^{\prime \prime }+9 y&=5 \\ \end{align*}

1.810

14860

12436

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

1.810

14861

2104

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

1.811

14862

2758

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

1.811

14863

8185

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

1.811

14864

8640

\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}
Using Laplace transform method.

1.811

14865

6201

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

1.812

14866

9277

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

1.812

14867

6291

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

1.813

14868

13798

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

1.813

14869

15283

\begin{align*} x^{\prime }&=2 x+4 y-2 z-2 \sinh \left (t \right ) \\ y^{\prime }&=4 x+2 y-2 z+10 \cosh \left (t \right ) \\ z^{\prime }&=-x+3 y+z+5 \\ \end{align*}

1.813

14870

15843

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

1.813

14871

16902

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

1.813

14872

11775

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

1.814

14873

13351

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

1.815

14874

14257

\begin{align*} N^{\prime }&=N-9 \,{\mathrm e}^{-t} \\ \end{align*}

1.815

14875

15409

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

1.815

14876

6708

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

1.816

14877

12640

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

1.816

14878

18025

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

1.816

14879

25829

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

1.817

14880

10321

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

1.819

14881

15281

\begin{align*} x^{\prime }&=-7 x+10 y+18 \,{\mathrm e}^{t} \\ y^{\prime }&=-10 x+9 y+37 \\ \end{align*}

1.819

14882

7662

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

1.820

14883

16207

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

1.820

14884

14968

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

1.821

14885

1618

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

1.822

14886

25461

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

1.822

14887

185

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

1.823

14888

6141

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

1.823

14889

22620

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

1.823

14890

23539

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

1.823

14891

3310

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

1.825

14892

8202

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

1.825

14893

16560

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y&=0 \\ \end{align*}

1.825

14894

8683

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

1.826

14895

2563

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

1.827

14896

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*}

1.827

14897

16361

\begin{align*} y^{\prime }-3 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}

1.827

14898

8048

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

1.828

14899

12595

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

1.828

14900

22474

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

1.828