2.3.229 Problems 22801 to 22900

Table 2.1031: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22801

25675

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

7.974

22802

1727

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

7.978

22803

26163

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

7.979

22804

19250

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

7.980

22805

22048

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

7.983

22806

12070

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

7.985

22807

4772

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

7.986

22808

18475

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

7.986

22809

15617

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

7.992

22810

17088

\begin{align*} y^{\prime }&=\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \\ \end{align*}

7.993

22811

11943

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

7.994

22812

27226

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

7.999

22813

3038

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

8.000

22814

4335

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

8.000

22815

4930

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

8.000

22816

12194

\begin{align*} y^{\prime }&=\frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\ \end{align*}

8.002

22817

27245

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

8.005

22818

11933

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

8.007

22819

14982

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

Series expansion around \(x=0\).

8.015

22820

22364

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

8.016

22821

21798

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

8.018

22822

5019

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

8.019

22823

7419

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

8.019

22824

13028

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

8.019

22825

14012

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

8.019

22826

11586

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

8.020

22827

17963

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

8.025

22828

22612

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

8.026

22829

5669

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

8.027

22830

5671

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

8.027

22831

18023

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

8.030

22832

14764

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

Series expansion around \(x=0\).

8.034

22833

3678

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

8.036

22834

24323

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

8.039

22835

3052

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

8.043

22836

9935

\begin{align*} 9 x^{2} y^{\prime \prime }-15 x y^{\prime }+7 \left (x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

8.044

22837

8381

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

8.046

22838

7464

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

8.052

22839

21975

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

8.059

22840

13380

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

8.061

22841

21991

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

8.061

22842

21088

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

8.062

22843

11951

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

8.064

22844

22504

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

8.065

22845

6122

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

8.066

22846

16979

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

8.067

22847

13677

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

8.068

22848

15640

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

8.071

22849

26318

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

8.071

22850

21185

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

8.073

22851

18497

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

8.074

22852

12542

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

8.076

22853

4883

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

8.078

22854

17209

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

8.079

22855

3471

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

8.081

22856

22402

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

8.090

22857

5611

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

8.092

22858

15230

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

Using Laplace transform method.

8.093

22859

27313

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

8.093

22860

18492

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

8.095

22861

15059

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

8.096

22862

5820

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

8.099

22863

4828

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

8.101

22864

14442

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

8.102

22865

17975

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

8.102

22866

12132

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

8.109

22867

6558

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

8.110

22868

11662

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

8.111

22869

5613

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

8.115

22870

16156

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

8.122

22871

27146

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

8.125

22872

8707

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

8.126

22873

12048

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

8.126

22874

11411

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

8.128

22875

12133

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

8.130

22876

18324

\begin{align*} y^{\prime \prime }+y&=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \\ \end{align*}

8.131

22877

20963

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

8.133

22878

11952

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

8.136

22879

11700

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

8.137

22880

16287

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

8.137

22881

13013

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

8.140

22882

17985

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

8.142

22883

8688

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

8.144

22884

6547

\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=-\left (1-y\right )^{3} \left (\operatorname {F0} \left (x \right )^{2}-\operatorname {G0} \left (x \right )^{2} y^{2}\right )-4 \left (1-y\right ) y^{2} \left (f \left (x \right )^{2}-g \left (x \right )^{2}+f^{\prime }\left (x \right )+g^{\prime }\left (x \right )\right )-4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2} \\ \end{align*}

8.148

22885

22516

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

8.148

22886

21560

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

8.150

22887

5859

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

8.152

22888

25895

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

8.152

22889

17634

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

8.154

22890

3425

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

8.155

22891

16218

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

8.156

22892

26289

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

8.157

22893

17633

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=\frac {1}{x^{5}} \\ \end{align*}

8.158

22894

5078

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

8.164

22895

21465

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

8.164

22896

8356

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

8.165

22897

18941

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

Using Laplace transform method.

8.165

22898

4222

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

8.166

22899

15401

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

8.170

22900

11940

\begin{align*} y^{\prime }&=-\frac {x}{4}+\frac {1}{4}+x^{2} \sqrt {x^{2}-2 x +1+8 y} \\ \end{align*}

8.174