2.3.187 Problems 18601 to 18700

Table 2.917: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

18601

1227

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

3.815

18602

4871

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

3.816

18603

21996

\begin{align*} \cos \left (x \right ) x +\left (1-6 y^{5}\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}

3.817

18604

17173

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

3.818

18605

9199

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

3.819

18606

11872

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

3.819

18607

4757

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

3.820

18608

19323

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

3.820

18609

25053

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

3.820

18610

1562

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

3.822

18611

25701

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

3.825

18612

22775

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

3.826

18613

11891

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

3.828

18614

15098

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

3.828

18615

4092

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

3.829

18616

6317

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

3.829

18617

15612

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

3.829

18618

17873

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

3.829

18619

20235

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

3.830

18620

22352

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

3.830

18621

11539

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

3.832

18622

11597

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

3.832

18623

23175

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

3.832

18624

23228

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

3.833

18625

13237

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

3.834

18626

16280

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

3.834

18627

9194

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

3.835

18628

19957

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

3.835

18629

2492

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

3.836

18630

19379

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

3.839

18631

26241

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

3.839

18632

15920

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

3.840

18633

21439

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

3.840

18634

25302

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 6 & 1\le t <3 \\ 0 & 3\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

3.840

18635

17981

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

3.841

18636

19750

\begin{align*} \theta ^{\prime \prime }-p^{2} \theta &=0 \\ \end{align*}

3.841

18637

24192

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

3.841

18638

24976

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

3.841

18639

3320

\begin{align*} 3 {y^{\prime }}^{4} x&=y {y^{\prime }}^{3}+1 \\ \end{align*}

3.842

18640

15873

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

3.842

18641

16250

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

3.842

18642

17858

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

3.842

18643

5463

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

3.843

18644

22042

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

3.843

18645

15931

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

3.844

18646

19017

\begin{align*} x_{1}^{\prime }&=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\ x_{2}^{\prime }&=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\ x_{3}^{\prime }&=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\ x_{4}^{\prime }&=-2 x_{2}+2 x_{3}+4 x_{4} \\ \end{align*}

3.844

18647

50

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

3.845

18648

3659

\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\ \end{align*}

3.846

18649

8775

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

3.846

18650

19681

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

3.846

18651

8838

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

3.847

18652

16215

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

3.847

18653

3524

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

3.848

18654

24235

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

3.848

18655

26167

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

3.848

18656

10151

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

3.849

18657

22808

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

3.849

18658

2948

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

3.852

18659

15924

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

3.852

18660

25606

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

3.853

18661

21418

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

3.854

18662

16235

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

3.856

18663

20109

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

3.857

18664

24990

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

3.860

18665

21787

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

3.861

18666

1561

\begin{align*} y^{\prime }+7 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 0 \\ \end{align*}

3.862

18667

5605

\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a&=0 \\ \end{align*}

3.864

18668

7678

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

3.865

18669

19142

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

3.865

18670

17147

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

3.866

18671

17413

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

3.866

18672

5225

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

3.867

18673

1554

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

3.868

18674

2972

\begin{align*} \cos \left (\theta \right ) r^{\prime }&=2+2 r \sin \left (\theta \right ) \\ \end{align*}

3.868

18675

1163

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

3.869

18676

10451

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

3.869

18677

17781

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

3.870

18678

14245

\begin{align*} 7 t^{2} x^{\prime }&=3 x-2 t \\ \end{align*}

3.871

18679

17210

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

3.871

18680

3528

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

3.873

18681

24061

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

3.873

18682

6580

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

3.874

18683

1791

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

3.875

18684

17160

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

3.875

18685

19941

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

3.875

18686

9651

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (-2+t \right )+\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

3.877

18687

112

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

3.878

18688

7402

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

3.878

18689

7495

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

3.879

18690

9121

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

3.879

18691

9773

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

3.880

18692

16037

\begin{align*} x^{\prime }&=\frac {y}{10} \\ y^{\prime }&=\frac {z}{5} \\ z^{\prime }&=\frac {2 x}{5} \\ \end{align*}

3.880

18693

21409

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

3.880

18694

2440

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

3.882

18695

2667

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

3.882

18696

24906

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

3.882

18697

26040

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

3.882

18698

25709

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

3.883

18699

17779

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

3.884

18700

21606

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

3.884