2.3.112 Problems 11101 to 11200

Table 2.797: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

11101

14560

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

0.862

11102

15571

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

0.862

11103

16812

\begin{align*} y^{\prime \prime }-16 y&=\delta \left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.862

11104

17515

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

0.862

11105

18663

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

0.862

11106

18804

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

0.862

11107

19698

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

0.862

11108

19987

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

0.862

11109

24102

\begin{align*} 6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.862

11110

26583

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

0.862

11111

2039

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

Series expansion around \(x=0\).

0.863

11112

3364

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

Series expansion around \(x=0\).

0.863

11113

4217

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

0.863

11114

4543

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

0.863

11115

6474

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

0.863

11116

10144

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

0.863

11117

14167

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

0.863

11118

19370

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

0.863

11119

21751

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

0.863

11120

1978

\begin{align*} 2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }+x \left (7 x^{2}+4\right ) y^{\prime }-\left (-3 x^{2}+1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.864

11121

2807

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

0.864

11122

14291

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

0.864

11123

18674

\begin{align*} x^{\prime }&=-\frac {4 x}{5}+2 y \\ y^{\prime }&=-x+\frac {6 y}{5} \\ \end{align*}

0.864

11124

20555

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

0.864

11125

21269

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

Series expansion around \(t=0\).

0.864

11126

500

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

Series expansion around \(x=0\).

0.865

11127

1959

\begin{align*} 9 x^{2} y^{\prime \prime }+9 x y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.865

11128

2046

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

Series expansion around \(x=0\).

0.865

11129

2719

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

0.865

11130

6781

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

0.865

11131

8534

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

Series expansion around \(x=0\).

0.865

11132

9705

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

0.865

11133

10192

\begin{align*} 2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.865

11134

12893

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

0.865

11135

15887

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

0.865

11136

4006

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

Series expansion around \(x=0\).

0.866

11137

11787

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

0.866

11138

12892

\begin{align*} x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y}&=0 \\ \end{align*}

0.866

11139

14738

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

Series expansion around \(x=0\).

0.866

11140

16911

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

Series expansion around \(x=-2\).

0.866

11141

17513

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

0.866

11142

19612

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

Series expansion around \(x=0\).

0.866

11143

21531

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=2 x -40 \cos \left (2 x \right ) \\ \end{align*}

0.866

11144

23546

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 x}}{x^{3}} \\ y \left (1\right ) &= 4 \,{\mathrm e}^{-3} \\ y^{\prime }\left (1\right ) &= -2 \,{\mathrm e}^{-3} \\ \end{align*}

0.866

11145

2021

\begin{align*} x^{2} \left (1-4 x \right ) y^{\prime \prime }+3 x \left (1-6 x \right ) y^{\prime }+\left (1-12 x \right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.867

11146

3873

\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2}+20 \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }&=3 x_{1}+x_{2}+12 \,{\mathrm e}^{t} \\ \end{align*}

0.867

11147

4033

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

Series expansion around \(x=0\).

0.867

11148

5792

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

0.867

11149

8798

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

0.867

11150

16811

\begin{align*} y^{\prime \prime }+16 y&=\delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.867

11151

21273

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

Series expansion around \(t=0\).

0.867

11152

23286

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

0.867

11153

2723

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

0.868

11154

2740

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

0.868

11155

3305

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

0.868

11156

4070

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

Series expansion around \(x=0\).

0.868

11157

8548

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

Series expansion around \(x=0\).

0.868

11158

9374

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

Series expansion around \(x=0\).

0.868

11159

10186

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

Series expansion around \(x=0\).

0.868

11160

10391

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

0.868

11161

16646

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{-x} \sin \left (x \right ) \\ \end{align*}

0.868

11162

18912

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

With initial conditions

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

0.868

11163

19010

\begin{align*} x_{1}^{\prime }&=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }&=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }&=3 x_{1}-2 x_{2}-2 x_{3} \\ \end{align*}

0.868

11164

21689

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

Series expansion around \(x=0\).

0.868

11165

23377

\begin{align*} x^{2} y^{\prime \prime }+\frac {7 x y^{\prime }}{2}-\frac {3 y}{2}&=0 \\ \end{align*}

0.868

11166

27422

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

0.868

11167

422

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

Series expansion around \(x=0\).

0.869

11168

1804

\begin{align*} y^{\prime \prime }+9 y&=\tan \left (3 x \right ) \\ \end{align*}

0.869

11169

2201

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y&=-{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \\ \end{align*}

0.869

11170

4042

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

Series expansion around \(x=0\).

0.869

11171

4046

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

Series expansion around \(x=0\).

0.869

11172

6301

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

0.869

11173

8516

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

Series expansion around \(x=0\).

0.869

11174

9375

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

Series expansion around \(x=0\).

0.869

11175

14925

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

0.869

11176

19117

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

0.869

11177

27075

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

Series expansion around \(x=0\).

0.869

11178

1956

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

Series expansion around \(x=0\).

0.870

11179

2250

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

0.870

11180

8890

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

0.870

11181

12310

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

0.870

11182

16057

\begin{align*} x^{\prime }&=\pi ^{2} x+\frac {187 y}{5} \\ y^{\prime }&=\sqrt {555}\, x+\frac {400617 y}{5000} \\ \end{align*}

With initial conditions

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

0.870

11183

17708

\begin{align*} \left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (5+x \right ) y^{\prime }+10 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.870

11184

23099

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

0.870

11185

23670

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

Series expansion around \(x=0\).

0.870

11186

24766

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

0.870

11187

26038

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

0.870

11188

27658

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

0.870

11189

9598

\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=10 x^{3}-2 x +5 \\ \end{align*}

Series expansion around \(x=0\).

0.871

11190

14403

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

0.871

11191

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*}

0.871

11192

25380

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}

0.871

11193

4016

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

Series expansion around \(x=0\).

0.872

11194

4074

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

Series expansion around \(x=0\).

0.872

11195

4595

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

Series expansion around \(x=0\).

0.872

11196

6684

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

0.872

11197

8514

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

Series expansion around \(x=0\).

0.872

11198

10449

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

0.872

11199

12547

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (x^{2} \ln \left (x \right )^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}}&=0 \\ \end{align*}

0.872

11200

14918

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

0.872