2.3.126 Problems 12501 to 12600

Table 2.825: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12501

19585

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

1.073

12502

20027

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

1.073

12503

2762

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

1.074

12504

4598

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

Series expansion around \(x=0\).

1.074

12505

14127

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

1.074

12506

14732

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

Series expansion around \(x=0\).

1.074

12507

22935

\begin{align*} x^{\prime }+x-5 y&=0 \\ y^{\prime }+4 x+5 y&=0 \\ \end{align*}

1.074

12508

25555

\begin{align*} y^{\prime \prime }+5 y^{\prime }+c y&={\mathrm e}^{i \omega t} \\ \end{align*}

1.074

12509

5466

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

1.075

12510

8515

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

Series expansion around \(x=0\).

1.075

12511

9901

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

Series expansion around \(x=0\).

1.075

12512

10887

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

1.075

12513

12309

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

1.075

12514

18979

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

1.075

12515

24926

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

1.075

12516

704

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

1.076

12517

2457

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

Series expansion around \(t=0\).

1.076

12518

2645

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

Series expansion around \(t=0\).

1.076

12519

4013

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

Series expansion around \(x=0\).

1.076

12520

7082

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

1.076

12521

12371

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

1.076

12522

13816

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

1.076

12523

14146

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

1.076

12524

16875

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

Series expansion around \(x=0\).

1.076

12525

21655

\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+\left (2 x +\frac {2}{x}\right ) y^{\prime }+2 x^{2} y&=\frac {4 x^{2}+2 x +10}{x^{4}} \\ \end{align*}

Series expansion around \(x=0\).

1.076

12526

24743

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

1.076

12527

7670

\begin{align*} x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x&=F \cos \left (\omega t \right ) \\ \end{align*}

1.077

12528

8263

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

1.077

12529

8617

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

Series expansion around \(x=0\).

1.077

12530

9537

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

Series expansion around \(x=0\).

1.077

12531

12632

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

1.077

12532

27035

\begin{align*} y^{\prime \prime \prime \prime }-11 y^{\prime \prime }+18 y&=f \left (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.

1.077

12533

1949

\begin{align*} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.078

12534

3013

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

1.078

12535

4018

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

Series expansion around \(x=0\).

1.078

12536

20903

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

Series expansion around \(x=0\).

1.078

12537

3877

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

1.079

12538

6497

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

1.079

12539

8989

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

Series expansion around \(x=0\).

1.079

12540

17719

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.079

12541

20673

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

1.079

12542

12999

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

1.080

12543

17495

\begin{align*} y^{\prime \prime }-12 y^{\prime }+37 y&={\mathrm e}^{6 t} \sec \left (t \right ) \\ \end{align*}

1.080

12544

20539

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

1.080

12545

22901

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

1.080

12546

1851

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

Series expansion around \(x=0\).

1.081

12547

20947

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

With initial conditions

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

1.081

12548

21300

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

1.081

12549

23567

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

1.081

12550

25972

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

1.081

12551

5468

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

1.082

12552

12896

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

1.082

12553

14743

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

Series expansion around \(x=1\).

1.082

12554

14781

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

1.082

12555

24792

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

1.082

12556

25379

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

With initial conditions

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

1.082

12557

1747

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

1.083

12558

1953

\begin{align*} 10 x^{2} \left (2 x^{2}+x +1\right ) y^{\prime \prime }+x \left (66 x^{2}+13 x +13\right ) y^{\prime }-\left (10 x^{2}+4 x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.083

12559

10542

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

1.083

12560

21532

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

1.083

12561

26470

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

1.083

12562

2027

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

Series expansion around \(x=0\).

1.084

12563

9533

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

Series expansion around \(x=0\).

1.084

12564

14879

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

1.084

12565

16608

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

1.084

12566

19636

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

Using Laplace transform method.

1.084

12567

21621

\begin{align*} \theta ^{\prime \prime }+4 \theta &=15 \cos \left (3 t \right ) \\ \theta \left (0\right ) &= 0 \\ \theta ^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.084

12568

22155

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

1.084

12569

1327

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

1.085

12570

1492

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

Using Laplace transform method.

1.085

12571

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*}

1.085

12572

8513

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

Series expansion around \(x=0\).

1.085

12573

24717

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

1.085

12574

25354

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

Series expansion around \(t=0\).

1.085

12575

26554

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

1.085

12576

4565

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

1.086

12577

9837

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.086

12578

13664

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

1.086

12579

15266

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=\frac {x}{2}-\frac {3 y}{2} \\ \end{align*}

1.086

12580

18027

\begin{align*} {y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\ \end{align*}

1.086

12581

18989

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

1.086

12582

25350

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

Series expansion around \(t=0\).

1.086

12583

4012

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

Series expansion around \(x=0\).

1.087

12584

7885

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

1.087

12585

15270

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

1.087

12586

1835

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (x +1\right ) y&=\left (x -1\right )^{3} {\mathrm e}^{x} \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}

1.088

12587

8935

\begin{align*} y^{\prime \prime \prime }-8 y&={\mathrm e}^{i x} \\ \end{align*}

1.088

12588

11896

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

1.088

12589

26509

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

1.088

12590

1749

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

1.089

12591

1824

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

1.089

12592

2463

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

Series expansion around \(t=0\).

1.089

12593

13413

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

1.089

12594

15182

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

1.089

12595

27660

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

1.089

12596

18986

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

1.090

12597

15656

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

1.091

12598

16409

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

1.091

12599

23783

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

1.091

12600

24927

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

1.091