2.3.42 Problems 4101 to 4200

Table 2.615: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

4101

10470

\begin{align*} \left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y&=0 \\ \end{align*}

0.321

4102

14992

\(\left [\begin {array}{cc} 7 & -2 \\ 26 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.321

4103

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.

0.321

4104

22915

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

0.321

4105

23642

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

0.321

4106

23648

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=27 t \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.321

4107

24055

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

0.321

4108

1374

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

0.322

4109

5397

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

0.322

4110

8610

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

0.322

4111

9617

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}
Using Laplace transform method.

0.322

4112

10521

\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \\ \end{align*}

0.322

4113

11032

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y&=0 \\ \end{align*}

0.322

4114

12995

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

0.322

4115

15009

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

0.322

4116

15197

\begin{align*} y^{\prime \prime \prime \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 ) &= \frac {\sqrt {2}}{2} \\ \end{align*}
Using Laplace transform method.

0.322

4117

15494

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

0.322

4118

16824

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

0.322

4119

19110

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

0.322

4120

19660

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

0.322

4121

431

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

0.323

4122

2031

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

0.323

4123

2056

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

0.323

4124

6677

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

0.323

4125

10631

\begin{align*} 4 x^{2} \left (x +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \\ \end{align*}

0.323

4126

14953

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

0.323

4127

16336

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

0.323

4128

20397

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

0.323

4129

23420

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

0.323

4130

430

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

0.324

4131

966

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

0.324

4132

1379

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

0.324

4133

3335

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

0.324

4134

3690

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

0.324

4135

4068

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

0.324

4136

4552

\begin{align*} x^{\prime }-2 x+y&=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x+y^{\prime }-2 y&=10 \,{\mathrm e}^{t} \sin \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.324

4137

6438

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

0.324

4138

6634

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

0.324

4139

10849

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

0.324

4140

12955

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

0.324

4141

13015

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

0.324

4142

18649

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

0.324

4143

22847

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

0.324

4144

922

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

0.325

4145

1797

\begin{align*} 36 y^{\prime }+36 y^{2}-12 y+1&=0 \\ \end{align*}

0.325

4146

2237

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

0.325

4147

5406

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

0.325

4148

8196

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

0.325

4149

10592

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

0.325

4150

16159

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

0.325

4151

16788

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=1 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.325

4152

18651

\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

0.325

4153

21217

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

0.325

4154

552

\begin{align*} x^{\prime \prime }+6 x^{\prime }+18 x&=\cos \left (2 t \right ) \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.326

4155

2232

\begin{align*} 4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-y^{\prime } x +y&=6 x \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ y^{\prime \prime }\left (1\right ) &= 4 \\ y^{\prime \prime \prime }\left (1\right ) &= -{\frac {37}{4}} \\ \end{align*}

0.326

4156

2297

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

0.326

4157

3417

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

0.326

4158

4168

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

0.326

4159

9062

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

0.326

4160

14791

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

0.326

4161

16767

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=7 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}
Using Laplace transform method.

0.326

4162

16801

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

0.326

4163

18371

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

0.326

4164

18689

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

0.326

4165

19587

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

0.326

4166

21210

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

0.326

4167

23438

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

0.326

4168

23614

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

0.326

4169

5647

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

0.327

4170

8738

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

0.327

4171

9359

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

0.327

4172

10461

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

0.327

4173

10639

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-2 x \left (3+14 x \right ) y^{\prime }+\left (6+100 x \right ) y&=0 \\ \end{align*}

0.327

4174

16823

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

0.327

4175

18648

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

0.327

4176

18910

\begin{align*} y_{1}^{\prime }&=-5 y_{1}+y_{2} \\ y_{2}^{\prime }&=-9 y_{1}+5 y_{2} \\ \end{align*}
With initial conditions
\begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= 0 \\ \end{align*}

0.327

4177

19035

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

0.327

4178

19590

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

0.327

4179

22820

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=6 \delta \left (-2+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.327

4180

22914

\begin{align*} x^{\prime }+5 x+3 y^{\prime }-11 y&=0 \\ x^{\prime }+3 x+y^{\prime }-7 y&=0 \\ \end{align*}

0.327

4181

25510

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

0.327

4182

1450

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

0.328

4183

1635

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

0.328

4184

2032

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

0.328

4185

3581

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

0.328

4186

6376

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

0.328

4187

7827

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

0.328

4188

10337

\begin{align*} y^{\prime } t +y&=0 \\ \end{align*}
Using Laplace transform method.

0.328

4189

10637

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

0.328

4190

14397

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

0.328

4191

14636

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \\ \end{align*}

0.328

4192

15973

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

0.328

4193

19214

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

0.328

4194

22882

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

0.328

4195

25368

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

0.328

4196

585

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

0.329

4197

964

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

0.329

4198

2030

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

0.329

4199

8578

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

0.329

4200

8850

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

0.329