2.3.117 Problems 11601 to 11700

Table 2.765: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11601

3184

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

0.637

11602

3981

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

0.637

11603

7167

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

0.637

11604

7197

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

0.637

11605

15287

\begin{align*} x^{\prime }&=7 x+y-1-6 \,{\mathrm e}^{t} \\ y^{\prime }&=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.637

11606

19663

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

0.637

11607

23795

\begin{align*} x^{\prime }&=5 x-6 y+1 \\ y^{\prime }&=6 x-7 y+1 \\ \end{align*}

0.637

11608

898

\begin{align*} y^{\prime \prime }+9 y&=2 \sec \left (3 x \right ) \\ \end{align*}

0.638

11609

1426

\begin{align*} x_{1}^{\prime }&=x_{1} \\ x_{2}^{\prime }&=-4 x_{1}+x_{2} \\ x_{3}^{\prime }&=3 x_{1}+6 x_{2}+2 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= -30 \\ \end{align*}

0.638

11610

3902

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

0.638

11611

4295

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

0.638

11612

4478

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

0.638

11613

5837

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

0.638

11614

6473

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

0.638

11615

6587

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

0.638

11616

8557

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (16 x^{4}+3\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.638

11617

9434

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

0.638

11618

11682

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

0.638

11619

14689

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

0.638

11620

15890

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

0.638

11621

17509

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

0.638

11622

18293

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

0.638

11623

18948

\begin{align*} y^{\prime \prime \prime \prime }-y&=\delta \left (-1+t \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.

0.638

11624

19039

\begin{align*} x_{1}^{\prime }&=-k_{1} x_{1} \\ x_{2}^{\prime }&=k_{1} x_{1}-k_{2} x_{2} \\ x_{3}^{\prime }&=k_{2} x_{2} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= m_{0} \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

0.638

11625

20212

\begin{align*} x^{\prime }+4 x+3 y&=t \\ y^{\prime }+2 x+5 y&={\mathrm e}^{t} \\ \end{align*}

0.638

11626

22710

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

0.638

11627

23611

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

0.638

11628

23725

\begin{align*} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+\frac {y}{16}&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.638

11629

3501

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

0.639

11630

7170

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

0.639

11631

8248

\begin{align*} 4 y+y^{\prime \prime }&=0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{6}\right ) &= 0 \\ \end{align*}

0.639

11632

13075

\begin{align*} 4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\ \end{align*}

0.639

11633

13687

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

0.639

11634

21150

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

0.639

11635

23568

\begin{align*} x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

0.639

11636

25585

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

0.639

11637

3584

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

0.640

11638

4567

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

0.640

11639

9433

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

0.640

11640

13675

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

0.640

11641

18768

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

0.640

11642

20351

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

0.640

11643

25304

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\operatorname {Heaviside}\left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.640

11644

25354

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

0.640

11645

25411

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

0.640

11646

593

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

0.641

11647

2105

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.641

11648

3375

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

0.641

11649

7313

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

0.641

11650

8603

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

0.641

11651

17990

\begin{align*} 4 {y^{\prime }}^{2}-9 x&=0 \\ \end{align*}

0.641

11652

19153

\begin{align*} x^{2} y^{2} y^{\prime \prime }-3 y^{2} y^{\prime } x +4 y^{3}+x^{6}&=0 \\ \end{align*}

0.641

11653

19495

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

0.641

11654

23924

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

0.641

11655

3698

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

0.642

11656

4396

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

0.642

11657

6552

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

0.642

11658

8103

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

0.642

11659

13037

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

0.642

11660

13876

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

0.642

11661

15390

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

0.642

11662

16122

\begin{align*} y^{\prime \prime }+6 y^{\prime }+20 y&=-3 \sin \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.642

11663

20944

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

0.642

11664

24141

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

0.642

11665

1340

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

0.643

11666

4015

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

0.643

11667

5981

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

0.643

11668

14393

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

0.643

11669

17378

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

0.643

11670

19654

\begin{align*} x^{\prime }&=5 x+2 y \\ y^{\prime }&=-17 x-5 y \\ \end{align*}

0.643

11671

21247

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

0.643

11672

22369

\begin{align*} i^{\prime }+5 i&=10 \\ i \left (0\right ) &= 0 \\ \end{align*}

0.643

11673

23098

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

0.643

11674

2451

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

0.644

11675

4537

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

0.644

11676

5937

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

0.644

11677

8090

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

0.644

11678

9823

\begin{align*} x^{6} {y^{\prime }}^{2}&=8 y^{\prime } x +16 y \\ \end{align*}

0.644

11679

10193

\begin{align*} \left (x +3\right ) x^{2} y^{\prime \prime }+5 x \left (x +1\right ) y^{\prime }-\left (1-4 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.644

11680

12988

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

0.644

11681

14686

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

0.644

11682

14987

\begin{align*} x^{\prime }&=5 x-4 y+{\mathrm e}^{3 t} \\ y^{\prime }&=x+y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -1 \\ \end{align*}

0.644

11683

18446

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

0.644

11684

18965

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

0.644

11685

20168

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

0.644

11686

20642

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

0.644

11687

25410

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

0.644

11688

987

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

0.645

11689

2048

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

0.645

11690

5530

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

0.645

11691

6233

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

0.645

11692

7375

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

0.645

11693

7377

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

0.645

11694

10441

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

0.645

11695

13102

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

0.645

11696

13103

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

0.645

11697

13961

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

0.645

11698

14409

\begin{align*} x^{\prime }&=-5 x+3 y+{\mathrm e}^{-t} \\ y^{\prime }&=2 x-10 y \\ \end{align*}

0.645

11699

16243

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

0.645

11700

22275

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=6 x_{1}+4 \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (1\right ) &= 0 \\ x_{2} \left (1\right ) &= 0 \\ \end{align*}

0.645