2.3.130 Problems 12901 to 13000

Table 2.803: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12901

6124

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

1.116

12902

10524

\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*}

1.116

12903

12632

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

1.116

12904

17719

\begin{align*} x^{2} y^{\prime \prime }+7 y^{\prime } x -7 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.116

12905

21934

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

1.116

12906

3219

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

1.117

12907

14649

\begin{align*} y^{\prime \prime }-10 y^{\prime }+29 y&=8 \,{\mathrm e}^{5 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

1.117

12908

14858

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

1.117

12909

19664

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

1.117

12910

25766

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

1.117

12911

3970

\begin{align*} -y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

1.118

12912

6054

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

1.118

12913

13961

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

1.118

12914

16519

\begin{align*} y^{\prime \prime }+16 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.118

12915

20722

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

1.118

12916

1239

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

1.119

12917

25410

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

1.119

12918

6068

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

1.120

12919

9903

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

1.120

12920

15237

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 1 & 1\le t <2 \\ -1 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.120

12921

23611

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

1.120

12922

23664

\begin{align*} y^{\prime \prime }+7 y^{\prime }+6 y&=250 \,{\mathrm e}^{t} \cos \left (t \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -7 \\ \end{align*}
Using Laplace transform method.

1.120

12923

2432

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

1.121

12924

9874

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

1.121

12925

10186

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

1.122

12926

11378

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

1.122

12927

20648

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

1.122

12928

21964

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

1.122

12929

22844

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

1.122

12930

25336

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

1.122

12931

6331

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

1.123

12932

9898

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

1.123

12933

21629

\begin{align*} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.123

12934

8354

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

1.124

12935

23568

\begin{align*} x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-4 x_{2}+2 x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 2 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

1.124

12936

121

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

1.125

12937

5023

\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\ \end{align*}

1.125

12938

5648

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

1.125

12939

5976

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

1.125

12940

12418

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

1.125

12941

23691

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

1.125

12942

9909

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

1.126

12943

15550

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

1.126

12944

15729

\begin{align*} y^{\prime \prime }+a^{2} y&=\delta \left (x -\pi \right ) f \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.126

12945

19007

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

1.126

12946

21600

\begin{align*} \left (x -1\right )^{2} y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }-14 y&=x^{3}-3 x^{2}+3 x -8 \\ \end{align*}

1.126

12947

23092

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

1.126

12948

9558

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

1.127

12949

10034

\begin{align*} \left (t^{2}+9\right ) y^{\prime \prime }+2 y^{\prime } t&=0 \\ y \left (3\right ) &= 2 \pi \\ y^{\prime }\left (3\right ) &= {\frac {2}{3}} \\ \end{align*}

1.127

12950

10191

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

1.127

12951

8047

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

1.128

12952

8504

\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}-25\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.128

12953

9813

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

1.128

12954

20152

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

1.128

12955

3265

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

1.129

12956

5582

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

1.129

12957

16623

\begin{align*} y^{\prime \prime }&=6 \,{\mathrm e}^{x} \sin \left (x \right ) x \\ \end{align*}

1.129

12958

22286

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

1.129

12959

23524

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

1.129

12960

24247

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

1.129

12961

22943

\begin{align*} x^{\prime }+2 x-y&=100 \sin \left (t \right ) \\ y^{\prime }-4 x-y&=36 t \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= -8 \\ y \left (0\right ) &= -21 \\ \end{align*}

1.130

12962

821

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

1.131

12963

216

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

1.132

12964

1330

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

1.132

12965

3978

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -\frac {\pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

1.132

12966

4455

\begin{align*} y^{\prime \prime }+6 y^{\prime }+10 y&=3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \\ \end{align*}

1.132

12967

9948

\begin{align*} 2 \left (x +5\right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.132

12968

12328

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

1.132

12969

15560

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

1.132

12970

23655

\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }-y&=34 \sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}
Using Laplace transform method.

1.132

12971

6574

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

1.133

12972

15503

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

1.133

12973

23418

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

1.133

12974

10199

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

1.134

12975

17710

\begin{align*} 5 y^{\prime \prime } x +8 y^{\prime }-y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.134

12976

19524

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

1.134

12977

2654

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

1.135

12978

9880

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

1.135

12979

10370

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

1.135

12980

10393

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

1.135

12981

12681

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

1.135

12982

22870

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-8\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.135

12983

9760

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

1.136

12984

9953

\begin{align*} 4 y x -\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.136

12985

13871

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

1.136

12986

25341

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

1.136

12987

7136

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

1.137

12988

7884

\begin{align*} 2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \\ \end{align*}

1.137

12989

14060

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

1.137

12990

7119

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

1.138

12991

8652

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.138

12992

9761

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

1.138

12993

19029

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

1.138

12994

23652

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=16 t \,{\mathrm e}^{-t}-15 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -9 \\ \end{align*}
Using Laplace transform method.

1.138

12995

9907

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

1.139

12996

9947

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

1.139

12997

10220

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

1.139

12998

16382

\begin{align*} y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\ \end{align*}

1.139

12999

15889

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

1.140

13000

21563

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

1.140