2.3.230 Problems 22901 to 23000

Table 2.991: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22901

20773

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

7.547

22902

17883

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

7.550

22903

19401

\begin{align*} \frac {3 y^{2}}{x^{2}+3 x}+\left (2 y \ln \left (\frac {5 x}{x +3}\right )+3 \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

7.568

22904

1203

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

7.579

22905

17319

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

7.580

22906

11576

\begin{align*} \left (-1+3 x +y\right )^{2} y^{\prime }-\left (-1+2 y\right ) \left (4 y+6 x -3\right )&=0 \\ \end{align*}

7.582

22907

17347

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

7.587

22908

7974

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

7.589

22909

12252

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

7.589

22910

5020

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

7.592

22911

5438

\begin{align*} 2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right )&=0 \\ \end{align*}

7.592

22912

9801

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

7.592

22913

14241

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

7.598

22914

11598

\begin{align*} \left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2}&=0 \\ \end{align*}

7.599

22915

18362

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

7.611

22916

16390

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

7.616

22917

3025

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

7.621

22918

6025

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

7.624

22919

19308

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

7.629

22920

11560

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

7.631

22921

7880

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

7.634

22922

12180

\begin{align*} y^{\prime }&=\frac {2 a \left (-y^{2}+4 a x -1\right )}{-y^{3}+4 a x y-y-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \\ \end{align*}

7.635

22923

24193

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

7.641

22924

19594

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

7.649

22925

22064

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

7.656

22926

12439

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

7.657

22927

21350

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

7.668

22928

18596

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

7.670

22929

25788

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

7.671

22930

21029

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

7.672

22931

4958

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

7.674

22932

19071

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

7.682

22933

24399

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

7.684

22934

11551

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

7.687

22935

12084

\begin{align*} y^{\prime }&=-\frac {-\frac {1}{x}-\textit {\_F1} \left (y+\frac {1}{x}\right )}{x} \\ \end{align*}

7.688

22936

19992

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

7.705

22937

5328

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

7.714

22938

7490

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

7.717

22939

11550

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

7.721

22940

24372

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

7.721

22941

17903

\begin{align*} x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {10 \pi }{3} \\ \end{align*}

7.723

22942

19318

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

7.723

22943

12485

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

7.724

22944

4959

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

7.728

22945

7250

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

7.731

22946

2519

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

7.737

22947

11557

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

7.743

22948

20246

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

7.743

22949

6906

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

7.744

22950

14193

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

7.745

22951

20968

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

7.750

22952

12454

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

7.751

22953

12160

\begin{align*} y^{\prime }&=-\frac {2 a}{-y-2 a -2 a y^{4}+16 y^{2} a^{2} x -32 a^{3} x^{2}-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}} \\ \end{align*}

7.754

22954

15966

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

7.754

22955

12020

\begin{align*} y^{\prime }&=\frac {2 a}{-x^{2} y+2 a y^{4} x^{2}-16 y^{2} a^{2} x +32 a^{3}} \\ \end{align*}

7.757

22956

11412

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

7.758

22957

11556

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

7.770

22958

12950

\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}&=0 \\ \end{align*}

7.770

22959

21633

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

7.770

22960

11802

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

7.771

22961

4809

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

7.773

22962

5326

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

7.773

22963

12100

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

7.779

22964

2360

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

7.780

22965

10078

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

7.783

22966

11925

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

7.784

22967

12069

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

7.795

22968

19146

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

7.795

22969

24321

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

7.797

22970

21094

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

7.807

22971

3030

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

7.810

22972

3468

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

7.812

22973

14236

\begin{align*} x^{\prime }&=6 t \left (x-1\right )^{{2}/{3}} \\ \end{align*}

7.812

22974

9456

\begin{align*} i^{\prime \prime }+2 i^{\prime }+3 i&=\left \{\begin {array}{cc} 30 & 0<t <2 \pi \\ 0 & 2 \pi \le t \le 5 \pi \\ 10 & 5 \pi <t <\infty \end {array}\right . \\ i \left (0\right ) &= 8 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

7.818

22975

21083

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

7.831

22976

740

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

7.845

22977

5145

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

7.846

22978

8166

\begin{align*} y^{\prime }&=25+y^{2} \\ \end{align*}

7.856

22979

20835

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

7.856

22980

7532

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

7.857

22981

20245

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

7.862

22982

5544

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

7.864

22983

25767

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

7.864

22984

11543

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

7.876

22985

21255

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

7.876

22986

7737

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

7.879

22987

13487

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

7.884

22988

17857

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

7.887

22989

19989

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

7.891

22990

11587

\begin{align*} x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 y x&=0 \\ \end{align*}

7.892

22991

12153

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

7.892

22992

12254

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

7.892

22993

11632

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

7.895

22994

15960

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

7.899

22995

20575

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

7.900

22996

12031

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

7.901

22997

18569

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

7.906

22998

7504

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

7.907

22999

13792

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

7.908

23000

16307

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

7.912