2.3.219 Problems 21801 to 21900

Table 2.969: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

21801

12364

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

4.963

21802

4317

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

4.964

21803

23354

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

4.965

21804

13019

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

4.967

21805

14449

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

4.967

21806

16374

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

4.967

21807

11859

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

4.970

21808

23245

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

4.970

21809

1217

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

4.971

21810

5224

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

4.971

21811

11663

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

4.971

21812

17229

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

4.973

21813

10257

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

4.974

21814

19348

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

4.975

21815

24145

\begin{align*} r^{\prime }&=-2 r t \\ r \left (0\right ) &= r_{0} \\ \end{align*}

4.975

21816

13285

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

4.978

21817

17877

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

4.978

21818

13229

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

4.980

21819

13252

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

4.981

21820

23869

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

4.982

21821

6470

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

4.983

21822

25210

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

4.988

21823

25507

\begin{align*} y^{\prime }&=\frac {4 t -y}{t -6 y} \\ \end{align*}

4.990

21824

15792

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

4.991

21825

21326

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

4.993

21826

11552

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

4.995

21827

11879

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

4.996

21828

1566

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

4.997

21829

3672

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

4.997

21830

22399

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

4.997

21831

19997

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

5.000

21832

19987

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

5.001

21833

4818

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

5.007

21834

5679

\begin{align*} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3}&=0 \\ \end{align*}

5.007

21835

1651

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

5.008

21836

19747

\begin{align*} v^{\prime }+2 u v&=2 u \\ \end{align*}

5.012

21837

4956

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

5.013

21838

13354

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

5.013

21839

12030

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

5.018

21840

19730

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

5.018

21841

25781

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

5.020

21842

15532

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

5.023

21843

24077

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

5.029

21844

16291

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

5.030

21845

19323

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

5.033

21846

5177

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

5.036

21847

21790

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

5.037

21848

2939

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

5.039

21849

17886

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

5.039

21850

20285

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

5.039

21851

3005

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

5.042

21852

15456

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

5.043

21853

21080

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

5.044

21854

18074

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

5.046

21855

11899

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

5.048

21856

1652

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

5.050

21857

1247

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

5.053

21858

12289

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

5.053

21859

13658

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

5.053

21860

5678

\begin{align*} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{4} \left (y-b \right )^{3}&=0 \\ \end{align*}

5.057

21861

18934

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2} \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

5.059

21862

20315

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

5.061

21863

21058

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

5.061

21864

4284

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

5.066

21865

12696

\begin{align*} y^{\prime \prime }&=-\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+\sin \left (x \right )^{2} x^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )} \\ \end{align*}

5.066

21866

5212

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

5.067

21867

1628

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

5.069

21868

11851

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

5.069

21869

13878

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

5.069

21870

1198

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

5.073

21871

13320

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

5.074

21872

3043

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

5.078

21873

6845

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

5.079

21874

6910

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

5.079

21875

22328

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

5.080

21876

12015

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

5.082

21877

21443

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

5.083

21878

18559

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

5.091

21879

4987

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

5.092

21880

17280

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

5.092

21881

23209

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

5.092

21882

6916

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

5.093

21883

24143

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

5.094

21884

12026

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

5.095

21885

8671

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

5.096

21886

4833

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

5.097

21887

1594

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

5.102

21888

15038

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

5.105

21889

12671

\begin{align*} y^{\prime \prime }&=-\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}-\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )} \\ \end{align*}

5.107

21890

5579

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

5.108

21891

4872

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

5.111

21892

6424

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

5.111

21893

6567

\begin{align*} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime }&=0 \\ \end{align*}

5.112

21894

16325

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

5.112

21895

15027

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

5.117

21896

24843

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

5.117

21897

14436

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

5.120

21898

20288

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

5.120

21899

7415

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

5.121

21900

15060

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

5.121