2.3.92 Problems 9101 to 9200

Table 2.733: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9101

18788

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

0.671

9102

19432

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

0.671

9103

19662

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

0.671

9104

21575

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=16 x^{3} {\mathrm e}^{3 x} \\ \end{align*}

0.671

9105

24933

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

0.671

9106

25580

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

0.671

9107

25761

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-12 x +8 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.671

9108

1994

\begin{align*} 8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.672

9109

3136

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 x} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.672

9110

3487

\begin{align*} f^{\prime \prime }+8 f^{\prime }+12 f&=12 \,{\mathrm e}^{-4 t} \\ f \left (0\right ) &= 0 \\ f^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.672

9111

10109

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

0.672

9112

13883

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

0.672

9113

14974

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

0.672

9114

16009

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

0.672

9115

17405

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.672

9116

24460

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

0.672

9117

24613

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

0.672

9118

25350

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

0.672

9119

1991

\begin{align*} 6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.673

9120

3724

\begin{align*} y^{\prime \prime }-y&=9 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.673

9121

5726

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

0.673

9122

7299

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=16 x^{2} {\mathrm e}^{-x} \\ \end{align*}

0.673

9123

7812

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

0.673

9124

8505

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

0.673

9125

9593

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

0.673

9126

15494

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

0.673

9127

22859

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

0.673

9128

8062

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

0.674

9129

9489

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

0.674

9130

10086

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

0.674

9131

12978

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

0.674

9132

14642

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=9 x^{2}+4 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.674

9133

15276

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

0.674

9134

15995

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

0.674

9135

16387

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

0.674

9136

17403

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

0.674

9137

18281

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

0.674

9138

18375

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

0.674

9139

24464

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

0.674

9140

24725

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

0.674

9141

4500

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

0.675

9142

4528

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= -2 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.675

9143

4562

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

0.675

9144

8497

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

0.675

9145

9778

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

0.675

9146

15700

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}-3 x^{2} \\ \end{align*}
Using Laplace transform method.

0.675

9147

16911

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

0.675

9148

17460

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=-2 \\ y \left (0\right ) &= {\frac {2}{3}} \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

0.675

9149

17788

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

0.675

9150

18888

\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=t^{2} {\mathrm e}^{t}+7 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.675

9151

25297

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

0.675

9152

3726

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

0.676

9153

20660

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

0.676

9154

25434

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

0.676

9155

3503

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

0.677

9156

7773

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

0.677

9157

8278

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

0.677

9158

10139

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

0.677

9159

14315

\begin{align*} x^{\prime \prime }-3 x^{\prime }-40 x&=2 \,{\mathrm e}^{-t} \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.677

9160

14802

\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\)

N/A

N/A

N/A

0.677

9161

14806

\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\)

N/A

N/A

N/A

0.677

9162

16597

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \\ \end{align*}

0.677

9163

16914

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

0.677

9164

16920

\begin{align*} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +\left (1-4 x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.677

9165

21714

\begin{align*} y^{\prime \prime }+4 y^{\prime }+8 y&=\sin \left (t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.677

9166

21749

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

0.677

9167

23086

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

0.677

9168

23626

\begin{align*} x^{\prime }&=7 x+4 y-4 z \\ y^{\prime }&=4 x-8 y-z \\ z^{\prime }&=-4 x-y-8 z \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 5 \\ z \left (0\right ) &= -1 \\ \end{align*}

0.677

9169

24760

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

0.677

9170

3911

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

0.678

9171

8563

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

0.678

9172

14808

\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\)

N/A

N/A

N/A

0.678

9173

15228

\begin{align*} y^{\prime \prime }+9 y&=24 \sin \left (t \right ) \left (\operatorname {Heaviside}\left (t \right )+\operatorname {Heaviside}\left (t -\pi \right )\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.678

9174

16614

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-4 \cos \left (x \right )+7 \sin \left (x \right ) \\ y \left (0\right ) &= 8 \\ y^{\prime }\left (0\right ) &= -5 \\ \end{align*}

0.678

9175

17026

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

0.678

9176

18817

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=-3 t \,{\mathrm e}^{-t} \\ \end{align*}

0.678

9177

20604

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

0.678

9178

20871

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=20 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.678

9179

21628

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

0.678

9180

21777

\begin{align*} x^{\prime }&=2 x-7 y \\ y^{\prime }&=3 x-8 y \\ \end{align*}

0.678

9181

23529

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \\ \end{align*}

0.678

9182

23573

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

0.678

9183

24680

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

0.678

9184

24709

\begin{align*} y^{\prime \prime }+25 y&=\sin \left (5 x \right ) \\ \end{align*}

0.678

9185

25939

\begin{align*} y^{\prime \prime }-y&=5 \,{\mathrm e}^{x} \\ \end{align*}

0.678

9186

25968

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

0.678

9187

236

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

0.679

9188

1813

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

0.679

9189

2664

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

0.679

9190

2731

\begin{align*} x_{1}^{\prime }&=-7 x_{1}+6 x_{3} \\ x_{2}^{\prime }&=5 x_{2} \\ x_{3}^{\prime }&=6 x_{1}+2 x_{3} \\ \end{align*}

0.679

9191

4169

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

0.679

9192

6297

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

0.679

9193

9694

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

0.679

9194

10140

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

0.679

9195

12682

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

0.679

9196

16869

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

0.679

9197

17595

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

0.679

9198

20904

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

0.679

9199

24805

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

0.679

9200

25975

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

0.679