2.3.96 Problems 9501 to 9600

Table 2.723: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9501

14229

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

1.053

9502

24747

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

1.053

9503

16430

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

1.054

9504

22350

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

1.054

9505

25460

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

1.054

9506

3825

\begin{align*} x_{1}^{\prime }&=x_{2} \\ x_{2}^{\prime }&=-b x_{1}-a x_{2} \\ \end{align*}

1.055

9507

6868

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

1.055

9508

15758

\begin{align*} y_{1}^{\prime }&=4 y_{1}+6 y_{2}+6 y_{3} \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+2 y_{3} \\ y_{3}^{\prime }&=-y_{1}-4 y_{2}-3 y_{3} \\ \end{align*}

1.055

9509

22771

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

1.055

9510

5539

\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\ \end{align*}

1.056

9511

7914

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

1.056

9512

7946

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

1.056

9513

8186

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

1.056

9514

9546

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

1.056

9515

11005

\begin{align*} 4 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+12 x^{2} \left (x +1\right ) y^{\prime }+\left (3 x^{2}+3 x +1\right ) y&=0 \\ \end{align*}

1.056

9516

15043

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

1.056

9517

20475

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

1.056

9518

23629

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

1.056

9519

3310

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

1.058

9520

10482

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

1.058

9521

14362

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

1.058

9522

19426

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

1.058

9523

21940

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

1.058

9524

2531

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

1.059

9525

8405

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

1.059

9526

10751

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

1.059

9527

2772

\begin{align*} x_{1}^{\prime }&=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\ x_{3}^{\prime }&=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \\ \end{align*}

1.060

9528

6469

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

1.060

9529

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 \(x=0\).

1.060

9530

25481

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

1.060

9531

3243

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

1.061

9532

3287

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

1.061

9533

3298

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

1.061

9534

10784

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

1.061

9535

19979

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

1.062

9536

23622

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

1.062

9537

9874

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

1.063

9538

10607

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}

1.063

9539

10677

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

1.063

9540

19010

\begin{align*} x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3} \\ \end{align*}

1.063

9541

10735

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

1.064

9542

11162

\begin{align*} y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\ \end{align*}

1.064

9543

15825

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

1.064

9544

16876

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

1.064

9545

10753

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

1.065

9546

20023

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

1.065

9547

3912

\begin{align*} x_{1}^{\prime }&=2 x_{1}+13 x_{2} \\ x_{2}^{\prime }&=-x_{1}-2 x_{2} \\ x_{3}^{\prime }&=2 x_{3}+4 x_{4} \\ x_{4}^{\prime }&=2 x_{4} \\ \end{align*}

1.066

9548

7355

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

1.066

9549

9943

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

1.066

9550

10680

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

1.066

9551

2079

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.067

9552

8988

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

1.067

9553

15094

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

1.067

9554

4403

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

1.068

9555

9863

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

1.068

9556

25477

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

1.068

9557

650

\begin{align*} x_{1}^{\prime }&=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }&=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }&=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }&=7 x_{1}+x_{2}+x_{3}+4 x_{4} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 3 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 3 \\ \end{align*}

1.069

9558

1610

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

1.069

9559

5299

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

1.069

9560

9959

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

1.069

9561

16705

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

1.069

9562

21165

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

1.069

9563

22854

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

1.069

9564

24006

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

1.069

9565

2761

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

1.070

9566

7566

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

1.070

9567

18739

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

1.071

9568

1945

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

1.072

9569

10741

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y&=0 \\ \end{align*}

1.072

9570

12941

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

1.072

9571

25704

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

1.072

9572

7445

\begin{align*} u^{\prime }&=\alpha \left (1-u\right )-\beta u \\ \end{align*}

1.073

9573

16274

\begin{align*} y^{\prime } x +\left (2+5 x \right ) y&=\frac {20}{x} \\ \end{align*}

1.073

9574

18048

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

1.073

9575

20719

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

1.073

9576

9407

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

1.074

9577

10712

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

1.074

9578

13705

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

1.074

9579

18082

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

1.074

9580

20949

\begin{align*} y^{\prime }&=y^{2}-6 y-16 \\ \end{align*}

1.074

9581

25420

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

1.074

9582

1183

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

1.075

9583

8529

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

1.075

9584

9400

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

1.075

9585

9956

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

1.075

9586

10181

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

1.075

9587

16049

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

1.075

9588

18065

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

1.075

9589

3279

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

1.076

9590

11828

\begin{align*} 16 y^{2} {y^{\prime }}^{3}+2 y^{\prime } x -y&=0 \\ \end{align*}

1.077

9591

15558

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

1.077

9592

15787

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

1.077

9593

11165

\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*}

1.078

9594

2700

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

1.079

9595

3316

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

1.079

9596

9707

\begin{align*} x^{\prime }&=x-12 y-14 z \\ y^{\prime }&=x+2 y-3 z \\ z^{\prime }&=x+y-2 z \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 6 \\ z \left (0\right ) &= -7 \\ \end{align*}

1.079

9597

15329

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

1.079

9598

11723

\begin{align*} y^{\prime }-1&=0 \\ \end{align*}

1.080

9599

15286

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

1.080

9600

18078

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

1.080