2.3.160 Problems 15901 to 16000

Table 2.851: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15901

6127

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

1.431

15902

7322

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

1.431

15903

8040

\begin{align*} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y&=\frac {1}{x^{3}} \\ \end{align*}

1.431

15904

14293

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

1.431

15905

14695

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

1.431

15906

17784

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

1.433

15907

15892

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

1.434

15908

25429

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

1.434

15909

12700

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

1.435

15910

16408

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

1.435

15911

19156

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

1.435

15912

22207

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

1.435

15913

5844

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

1.436

15914

18532

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

1.436

15915

20375

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

1.436

15916

801

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

1.437

15917

3598

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

1.437

15918

8276

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

1.437

15919

8651

\begin{align*} 4 y^{\prime \prime }+24 y^{\prime }+37 y&=17 \,{\mathrm e}^{-t}+\delta \left (t -\frac {1}{2}\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.437

15920

3155

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

1.438

15921

15109

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

1.438

15922

23113

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

1.438

15923

8094

\begin{align*} \left (1-x \right ) x^{2} y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.439

15924

6030

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

1.440

15925

20497

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

1.440

15926

771

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

1.441

15927

6027

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

1.441

15928

6429

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

1.441

15929

13496

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

1.441

15930

2534

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

1.442

15931

3520

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

1.442

15932

23740

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

1.442

15933

24100

\begin{align*} 25 x^{2} y^{\prime \prime }+\left (4+2 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.442

15934

24966

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

1.443

15935

21027

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

1.444

15936

24985

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

1.444

15937

24996

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

1.444

15938

4048

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

1.446

15939

5220

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

1.446

15940

6563

\begin{align*} 2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime }&=\operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (-1+\operatorname {a2} \right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 y x \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 y x +3 y^{2}\right ) {y^{\prime }}^{2} \\ \end{align*}

1.446

15941

14968

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

1.446

15942

3597

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

1.447

15943

4659

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

1.447

15944

16684

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

1.447

15945

1716

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

1.448

15946

4571

\begin{align*} x_{1}^{\prime }&=-x_{1}+8 x_{2}+9 t \\ x_{2}^{\prime }&=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \\ \end{align*}

1.448

15947

5044

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

1.448

15948

21447

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

1.448

15949

4438

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

1.449

15950

5836

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

1.449

15951

17000

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}

1.449

15952

22995

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

1.449

15953

23739

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

1.449

15954

92

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

1.450

15955

10202

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

1.450

15956

3226

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

1.451

15957

14712

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \\ \end{align*}

1.451

15958

15122

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

1.451

15959

17645

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

1.451

15960

19618

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\ \end{align*}
Series expansion around \(x=-1\).

1.451

15961

3574

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

1.452

15962

7393

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

1.452

15963

8463

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

1.452

15964

18630

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

1.452

15965

24068

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

1.452

15966

25727

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (\pi \right ) &= 5 \\ \end{align*}

1.452

15967

798

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

1.454

15968

4027

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

1.454

15969

10429

\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \\ \end{align*}

1.454

15970

17781

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

1.454

15971

4699

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

1.455

15972

8743

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

1.455

15973

13018

\begin{align*} \left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2}&=0 \\ \end{align*}

1.455

15974

19003

\begin{align*} x_{1}^{\prime }&=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\ x_{2}^{\prime }&=-3 x_{2} \\ x_{3}^{\prime }&=x_{1}-x_{3}-x_{5} \\ x_{4}^{\prime }&=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\ x_{5}^{\prime }&=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \\ \end{align*}

1.455

15975

24841

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

1.455

15976

25821

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

1.455

15977

7677

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

1.456

15978

7951

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

1.456

15979

8042

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

1.456

15980

22523

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

1.456

15981

4038

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

1.457

15982

4960

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

1.457

15983

13889

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

1.457

15984

16326

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

1.457

15985

3774

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=9 \ln \left (x \right ) \\ \end{align*}

1.458

15986

15900

\begin{align*} y^{\prime }&=-4 y+3 \,{\mathrm e}^{-t} \\ \end{align*}

1.458

15987

20228

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

1.458

15988

8260

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

1.460

15989

8778

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

1.460

15990

11807

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

1.460

15991

15061

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

1.461

15992

22611

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

1.461

15993

24099

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

1.461

15994

2656

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

1.462

15995

10111

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

1.462

15996

11356

\begin{align*} y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\ \end{align*}

1.462

15997

13766

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

1.462

15998

14902

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

1.462

15999

19420

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

1.462

16000

1836

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

1.463