2.3.82 Problems 8101 to 8200

Table 2.737: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

8101

14821

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=20 \sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= -2 \\ \end{align*}

Using Laplace transform method.

1.031

8102

3584

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

1.032

8103

8966

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

Series expansion around \(x=0\).

1.032

8104

19511

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

1.032

8105

21857

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

1.032

8106

24487

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

1.032

8107

2603

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=\sin \left (t \right )+{\mathrm e}^{2 t} t \\ \end{align*}

1.033

8108

3380

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

Series expansion around \(x=0\).

1.033

8109

15272

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

1.033

8110

16627

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

1.033

8111

20132

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

1.033

8112

20807

\begin{align*} x^{\prime }-7 x+y&=0 \\ y^{\prime }-2 x-5 y&=0 \\ \end{align*}

1.033

8113

23362

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=0 \\ \end{align*}

1.033

8114

3365

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

Series expansion around \(x=0\).

1.034

8115

23834

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

1.034

8116

2430

\begin{align*} t^{2} y^{\prime \prime }-5 y^{\prime } t +9 y&=0 \\ \end{align*}

1.035

8117

6435

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

1.035

8118

6501

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

1.035

8119

9028

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

1.035

8120

21209

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

1.035

8121

21774

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

1.035

8122

2067

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

Series expansion around \(x=0\).

1.036

8123

2708

\begin{align*} x^{\prime }&=y+\textit {f\_1} \left (t \right ) \\ y^{\prime }&=-x+f_{2} \left (t \right ) \\ \end{align*}

With initial conditions

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

1.036

8124

7757

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

1.036

8125

14408

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

With initial conditions

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

1.036

8126

17820

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.036

8127

19778

\begin{align*} v^{\prime \prime }+\frac {2 v^{\prime }}{r}&=0 \\ \end{align*}

1.036

8128

21138

\begin{align*} x^{\prime \prime }-4 x^{\prime }+13 x&=20 \,{\mathrm e}^{t} \\ \end{align*}

1.036

8129

23526

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

1.036

8130

1385

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

Series expansion around \(x=1\).

1.037

8131

10029

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

1.037

8132

10386

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

1.037

8133

15214

\begin{align*} 4 y^{\prime \prime }+5 y^{\prime }+4 y&=3 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

1.037

8134

17482

\begin{align*} y^{\prime \prime }+16 y^{\prime }&=t \\ \end{align*}

1.037

8135

22298

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=6 \,{\mathrm e}^{x} \\ \end{align*}

1.037

8136

23336

\begin{align*} 9 y^{\prime \prime }-6 y^{\prime }+y&=0 \\ \end{align*}

1.037

8137

23673

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

Series expansion around \(x=0\).

1.037

8138

1345

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

1.038

8139

3903

\begin{align*} x_{1}^{\prime }&=2 x_{1}-4 x_{2}+3 x_{3} \\ x_{2}^{\prime }&=-9 x_{1}-3 x_{2}-9 x_{3} \\ x_{3}^{\prime }&=4 x_{1}+4 x_{2}+3 x_{3} \\ \end{align*}

1.038

8140

21646

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

Series expansion around \(x=0\).

1.038

8141

1850

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

Series expansion around \(x=0\).

1.039

8142

2564

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

1.039

8143

3364

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

Series expansion around \(x=0\).

1.039

8144

6162

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

1.039

8145

7823

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

Using Laplace transform method.

1.039

8146

10385

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

1.039

8147

15715

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

Using Laplace transform method.

1.039

8148

20367

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

1.039

8149

21898

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

1.039

8150

228

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \\ y \left (2\right ) &= 10 \\ y^{\prime }\left (2\right ) &= 15 \\ \end{align*}

1.040

8151

1985

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

Series expansion around \(x=0\).

1.040

8152

4433

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

1.040

8153

4597

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

Series expansion around \(x=0\).

1.040

8154

13723

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

1.040

8155

19043

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }&=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \\ \end{align*}

1.040

8156

21536

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

1.040

8157

23031

\begin{align*} z^{\prime \prime }+8 z^{\prime }+16 z&=0 \\ \end{align*}

1.040

8158

12990

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

1.041

8159

14103

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

1.041

8160

15693

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

1.041

8161

18853

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

1.041

8162

10388

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

1.042

8163

14600

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

1.042

8164

15575

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

1.042

8165

19060

\begin{align*} x_{1}^{\prime }&=x_{1}+x_{2} \\ x_{2}^{\prime }&=-14 x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }&=15 x_{1}+5 x_{2}-2 x_{3} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 5 \\ x_{2} \left (0\right ) &= 5 \\ x_{3} \left (0\right ) &= -4 \\ \end{align*}

1.042

8166

22289

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

1.042

8167

23363

\begin{align*} 4 y^{\prime \prime }+8 y^{\prime }+4 y&=0 \\ \end{align*}

1.042

8168

4123

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

1.043

8169

7766

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

1.043

8170

9979

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

1.043

8171

14879

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

1.043

8172

14924

\begin{align*} 2 z^{\prime \prime }+7 z^{\prime }-4 z&=0 \\ z \left (0\right ) &= 0 \\ z^{\prime }\left (0\right ) &= 9 \\ \end{align*}

1.043

8173

16062

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

1.043

8174

16651

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{3 x} \\ \end{align*}

1.043

8175

22642

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

1.043

8176

25966

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

1.043

8177

6531

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

1.044

8178

7762

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\ \end{align*}

1.044

8179

10162

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

1.044

8180

10522

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \\ \end{align*}

1.044

8181

15984

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

1.044

8182

21740

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

1.044

8183

2432

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

1.045

8184

5676

\begin{align*} 3 {y^{\prime }}^{5}-y y^{\prime }+1&=0 \\ \end{align*}

1.045

8185

6574

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

1.045

8186

8924

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

1.045

8187

19595

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

Series expansion around \(x=0\).

1.045

8188

22252

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

Using Laplace transform method.

1.045

8189

1957

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

Series expansion around \(x=0\).

1.046

8190

10401

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

1.046

8191

16169

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

1.046

8192

17531

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

1.046

8193

18396

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

1.046

8194

24479

\begin{align*} y^{\prime \prime \prime }+7 y^{\prime \prime }+19 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= -12 \\ \end{align*}

1.046

8195

3889

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

1.047

8196

5904

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

1.047

8197

6401

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

1.047

8198

6444

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

1.047

8199

9230

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

1.047

8200

17429

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

1.047