2.3.139 Problems 13801 to 13900

Table 2.821: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

13801

1916

\begin{align*} \left (\beta \,x^{2}+x \alpha +1\right ) y^{\prime \prime }+\left (\delta x +\gamma \right ) y^{\prime }+\epsilon y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.340

13802

13672

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

1.340

13803

21408

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

1.340

13804

9872

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

1.341

13805

17523

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

1.341

13806

20608

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

1.341

13807

25412

\begin{align*} y+y^{\prime }&=\operatorname {Heaviside}\left (t -10\right ) \\ \end{align*}

1.341

13808

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*}

1.342

13809

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*}

1.342

13810

17790

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

1.342

13811

22285

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

1.343

13812

23621

\begin{align*} x^{\prime }&=-10 x+y+7 z \\ y^{\prime }&=-9 x+4 y+5 z \\ z^{\prime }&=-17 x+y+12 z \\ \end{align*}

1.343

13813

25310

\begin{align*} y^{\prime \prime }+4 y&=\delta \left (t -\pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.343

13814

12846

\begin{align*} y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \\ \end{align*}

1.344

13815

7172

\begin{align*} \left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.345

13816

8056

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

1.345

13817

8976

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

1.345

13818

10440

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

1.345

13819

13742

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

1.345

13820

12429

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

1.346

13821

18048

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

1.346

13822

20472

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

1.346

13823

16512

\begin{align*} y^{\prime \prime }+25 y&=0 \\ \end{align*}

1.347

13824

23741

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

1.347

13825

12311

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

1.348

13826

14772

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

1.348

13827

22786

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

1.348

13828

25893

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

1.348

13829

5570

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

1.349

13830

168

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

1.350

13831

657

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

1.350

13832

24113

\begin{align*} 9 x^{2} y^{\prime \prime }+\left (x^{2}-15 x \right ) y^{\prime }+7 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.350

13833

494

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

1.351

13834

4523

\begin{align*} y^{\prime \prime }+4 y&=8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

1.351

13835

20861

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

1.351

13836

24946

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

1.351

13837

25414

\begin{align*} y^{\prime }-5 y&=3 \operatorname {Heaviside}\left (t -4\right ) \\ \end{align*}

1.351

13838

807

\begin{align*} y^{\prime \prime }-y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

1.352

13839

16409

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

1.352

13840

19757

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

1.352

13841

22751

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

1.352

13842

9920

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

1.353

13843

11821

\begin{align*} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\ \end{align*}

1.353

13844

19703

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

1.353

13845

25464

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

1.353

13846

2193

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y&={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \\ \end{align*}

1.354

13847

4579

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}

1.354

13848

9869

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

1.354

13849

14689

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

1.354

13850

18630

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

1.354

13851

21858

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

1.354

13852

3234

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 y^{\prime } x -6 y&=\cos \left (\ln \left (x \right )\right ) \\ \end{align*}

1.355

13853

6444

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

1.355

13854

1262

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

1.356

13855

9256

\begin{align*} 4 y+y^{\prime \prime }&=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \\ \end{align*}

1.356

13856

23733

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

1.356

13857

6355

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

1.357

13858

6510

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

1.357

13859

8333

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

1.357

13860

14879

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

1.357

13861

12640

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

1.358

13862

16811

\begin{align*} y^{\prime \prime }+16 y&=\delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.358

13863

26193

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

1.358

13864

2765

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

1.359

13865

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*}

1.359

13866

20008

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

1.359

13867

23565

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

1.360

13868

7629

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

1.361

13869

9776

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

1.361

13870

18948

\begin{align*} y^{\prime \prime \prime \prime }-y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.361

13871

22789

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

1.361

13872

23938

\begin{align*} y^{\prime }&=x^{2}+6 y+4 z \\ z^{\prime }&=y+3 z \\ \end{align*}

1.361

13873

12445

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

1.362

13874

26098

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

1.362

13875

8458

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

1.363

13876

745

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

1.364

13877

8683

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

1.364

13878

23597

\begin{align*} c_{1}^{\prime }&=-\frac {k c_{1}}{V_{1}}+\frac {k c_{2}}{V_{1}} \\ c_{2}^{\prime }&=\frac {k c_{1}}{V_{2}}-\frac {k c_{2}}{V_{2}} \\ \end{align*}

1.365

13879

7192

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

1.366

13880

13107

\begin{align*} x^{\prime }&=c y-b z \\ y^{\prime }&=a z-c x \\ z^{\prime }&=b x-a y \\ \end{align*}

1.366

13881

14333

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

1.366

13882

6964

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

1.367

13883

20452

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

1.367

13884

5644

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

1.368

13885

20437

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

1.368

13886

21080

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

1.368

13887

24895

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

1.368

13888

8448

\begin{align*} L i^{\prime }+R i&=E \\ i \left (0\right ) &= i_{0} \\ \end{align*}

1.369

13889

10444

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

1.369

13890

11346

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

1.369

13891

17455

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

1.369

13892

17727

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

1.369

13893

660

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

1.370

13894

8300

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

1.370

13895

9915

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

1.370

13896

17524

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

1.370

13897

20424

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

1.370

13898

5724

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

1.371

13899

20087

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

1.371

13900

22459

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

1.371