2.3.219 Problems 21801 to 21900

Table 2.981: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

21801

8699

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

8.519

21802

7855

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

8.521

21803

24190

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

8.531

21804

13906

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

8.535

21805

15857

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

8.536

21806

4763

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

8.539

21807

6415

\begin{align*} \left (c \,x^{2}+2 b x +a \right )^{{3}/{2}} y^{\prime \prime }&=f \left (\frac {x}{\sqrt {c \,x^{2}+2 b x +a}}\right ) \\ \end{align*}

8.540

21808

19423

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

8.541

21809

7157

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

8.544

21810

19099

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

8.551

21811

17258

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

8.555

21812

14494

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

8.556

21813

6048

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

8.558

21814

13435

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

8.569

21815

3468

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

8.574

21816

7497

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

8.576

21817

25781

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

8.576

21818

11918

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

8.583

21819

20243

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

8.585

21820

8380

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

8.586

21821

23892

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

8.587

21822

12992

\begin{align*} 8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2}&=0 \\ \end{align*}

8.595

21823

25802

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

8.599

21824

17310

\begin{align*} y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\ \end{align*}

8.602

21825

5030

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

8.605

21826

11914

\begin{align*} y^{\prime }&=\frac {x^{2} \left (1+2 \sqrt {x^{3}-6 y}\right )}{2} \\ \end{align*}

8.608

21827

7499

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

8.611

21828

14472

\begin{align*} 8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{4} \\ \end{align*}

8.619

21829

23128

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

8.619

21830

14179

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

8.621

21831

17296

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

8.628

21832

21861

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

8.633

21833

4731

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

8.635

21834

17205

\begin{align*} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \\ \end{align*}

8.635

21835

20259

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

8.635

21836

6995

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

8.638

21837

14272

\begin{align*} w^{\prime }&=t w+t^{3} w^{3} \\ \end{align*}

8.638

21838

14222

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

8.640

21839

11840

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

8.643

21840

4435

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

8.647

21841

10287

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

8.647

21842

5338

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

8.655

21843

23146

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

8.655

21844

14929

\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

8.660

21845

11575

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

8.662

21846

12256

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

8.662

21847

22317

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

8.662

21848

6908

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

8.665

21849

9017

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

8.668

21850

22455

\begin{align*} r^{\prime }&=t -\frac {r}{3 t} \\ r \left (1\right ) &= 1 \\ \end{align*}

8.671

21851

22774

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

8.671

21852

9791

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

8.680

21853

14726

\begin{align*} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y&=0 \\ \end{align*}

8.680

21854

16684

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=6 x^{3} \\ \end{align*}

8.681

21855

13052

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

8.686

21856

12484

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

8.687

21857

11911

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

8.690

21858

8728

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

8.691

21859

26153

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

8.693

21860

6846

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

8.696

21861

5022

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

8.700

21862

18614

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

8.700

21863

4930

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

8.701

21864

13000

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

8.701

21865

7543

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

8.709

21866

23142

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

8.714

21867

23886

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

8.715

21868

22404

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

8.722

21869

3230

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

8.727

21870

11954

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

8.728

21871

16979

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

8.728

21872

4652

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

8.734

21873

23850

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

8.735

21874

17209

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

8.736

21875

11489

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

8.737

21876

24229

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

8.737

21877

17938

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

8.743

21878

24403

\begin{align*} 4 x +3 y-7+\left (4 x +3 y+1\right ) y^{\prime }&=0 \\ \end{align*}

8.746

21879

5011

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

8.749

21880

4398

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

8.750

21881

20814

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

8.750

21882

4359

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

8.756

21883

20828

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

8.756

21884

8469

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

8.757

21885

20309

\begin{align*} {x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\ x \left (0\right ) &= 0 \\ \end{align*}

8.758

21886

14823

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

8.759

21887

20225

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

8.763

21888

13466

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

8.764

21889

22534

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

8.764

21890

17113

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

8.766

21891

3229

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

8.767

21892

14456

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

8.770

21893

24273

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

8.778

21894

23056

\begin{align*} \frac {r^{\prime }}{r}&=\tan \left (\theta \right ) \\ \end{align*}

8.781

21895

732

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

8.785

21896

2988

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

8.787

21897

12999

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

8.790

21898

5548

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

8.792

21899

12855

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

8.794

21900

22381

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

8.795