2.3.62 Problems 6101 to 6200

Table 2.697: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

6101

23045

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

0.470

6102

23978

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

0.470

6103

23981

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

0.470

6104

24104

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

Series expansion around \(x=0\).

0.470

6105

25637

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

Using Laplace transform method.

0.470

6106

25669

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

0.470

6107

26568

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

0.470

6108

26950

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

0.470

6109

26968

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=20 x^{2}+2 x -8 \\ \end{align*}

0.470

6110

342

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

0.471

6111

796

\begin{align*} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\ \end{align*}

0.471

6112

2718

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

0.471

6113

2824

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

0.471

6114

3169

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

0.471

6115

3178

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

0.471

6116

3494

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

0.471

6117

7081

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \\ \end{align*}

0.471

6118

7659

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

Series expansion around \(x=0\).

0.471

6119

7765

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=100 \sin \left (4 x \right ) \\ \end{align*}

0.471

6120

8101

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

Series expansion around \(x=0\).

0.471

6121

8494

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

Series expansion around \(x=0\).

0.471

6122

8573

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

Series expansion around \(x=0\).

0.471

6123

9715

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

0.471

6124

10296

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

0.471

6125

10341

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

Using Laplace transform method.

0.471

6126

10359

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

Series expansion around \(x=0\).

0.471

6127

12839

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

0.471

6128

16118

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=-3 \sin \left (2 t \right ) \\ \end{align*}

0.471

6129

16525

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

0.471

6130

20047

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

0.471

6131

22889

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

0.471

6132

23074

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

0.471

6133

24870

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

0.471

6134

25643

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

Using Laplace transform method.

0.471

6135

26552

\begin{align*} y^{\prime \prime }+4 y^{\prime }+3 y&=9 \,{\mathrm e}^{-3 x} \\ \end{align*}

0.471

6136

27064

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

Series expansion around \(x=0\).

0.471

6137

2241

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

0.472

6138

4510

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

0.472

6139

7645

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

Series expansion around \(x=1\).

0.472

6140

9689

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

0.472

6141

10237

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

0.472

6142

10615

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

0.472

6143

16113

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

0.472

6144

16179

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

0.472

6145

21627

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

Series expansion around \(x=0\).

0.472

6146

23578

\begin{align*} N_{1}^{\prime }&=4 N_{1}-6 N_{2} \\ N_{2}^{\prime }&=8 N_{1}-10 N_{2} \\ \end{align*}

With initial conditions

\begin{align*} N_{1} \left (0\right ) &= 100000 \\ N_{2} \left (0\right ) &= 1000 \\ \end{align*}

0.472

6147

24583

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

0.472

6148

26739

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

With initial conditions

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

0.472

6149

27655

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

0.472

6150

515

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

0.473

6151

880

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

0.473

6152

1788

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

0.473

6153

2368

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

0.473

6154

2414

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

Series expansion around \(t=0\).

0.473

6155

2623

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

Series expansion around \(t=0\).

0.473

6156

3391

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

Series expansion around \(x=0\).

0.473

6157

12849

\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y}&=0 \\ \end{align*}

0.473

6158

14199

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

0.473

6159

14563

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}

0.473

6160

14577

\begin{align*} 3 y^{\prime \prime }-14 y^{\prime }-5 y&=0 \\ \end{align*}

0.473

6161

16001

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

With initial conditions

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

0.473

6162

16126

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&={\mathrm e}^{-t} \cos \left (t \right ) \\ \end{align*}

0.473

6163

19587

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

Series expansion around \(x=0\).

0.473

6164

20893

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

Series expansion around \(x=0\).

0.473

6165

21636

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

Series expansion around \(x=0\).

0.473

6166

23460

\begin{align*} y^{\prime \prime }-13 y^{\prime }+36 y&={\mathrm e}^{4 x} x \\ \end{align*}

0.473

6167

24022

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

0.473

6168

25079

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=50 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

0.473

6169

25084

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

Using Laplace transform method.

0.473

6170

25816

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

0.473

6171

27578

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

0.473

6172

836

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

0.474

6173

872

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

0.474

6174

1392

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

Series expansion around \(x=0\).

0.474

6175

2727

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

0.474

6176

4069

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

Series expansion around \(x=0\).

0.474

6177

4431

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

0.474

6178

7633

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

Series expansion around \(x=0\).

0.474

6179

7840

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

Series expansion around \(x=0\).

0.474

6180

8116

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

Series expansion around \(x=0\).

0.474

6181

8197

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

0.474

6182

8338

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

0.474

6183

8498

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

Series expansion around \(x=0\).

0.474

6184

10340

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

Using Laplace transform method.

0.474

6185

13060

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

0.474

6186

14182

\begin{align*} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\ \end{align*}

0.474

6187

16627

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-3 \,{\mathrm e}^{-2 x} \\ \end{align*}

0.474

6188

17396

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

0.474

6189

19566

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

0.474

6190

19760

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime }&=17 x^{6} \\ \end{align*}

0.474

6191

19777

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

0.474

6192

21660

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

Series expansion around \(x=0\).

0.474

6193

22164

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

0.474

6194

24081

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+20 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.474

6195

24592

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

0.474

6196

636

\begin{align*} x_{1}^{\prime }&=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }&=100 x_{1}-60 x_{2} \\ \end{align*}

0.475

6197

657

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

0.475

6198

3233

\begin{align*} 3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y&=\frac {4}{x^{2}} \\ \end{align*}

0.475

6199

3834

\begin{align*} x_{1}^{\prime }&=-2 x_{1}-7 x_{2} \\ x_{2}^{\prime }&=-x_{1}+4 x_{2} \\ \end{align*}

0.475

6200

8559

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

Series expansion around \(x=0\).

0.475