2.3.122 Problems 12101 to 12200

Table 2.817: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12101

19862

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

1.003

12102

21163

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

1.003

12103

24736

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

1.003

12104

25987

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

1.003

12105

26057

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

1.003

12106

2203

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

1.004

12107

3382

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

Series expansion around \(x=0\).

1.004

12108

13666

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

1.004

12109

22222

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

Series expansion around \(x=0\).

1.004

12110

27172

\begin{align*} x_{1}^{\prime }&=x_{1}-3 x_{2}+t \,{\mathrm e}^{-2 t} \\ x_{2}^{\prime }&=3 x_{1}-5 x_{2}+t \,{\mathrm e}^{-2 t} \\ x_{3}^{\prime }&=4 x_{1}+7 x_{2}-2 x_{3}+t^{2} {\mathrm e}^{-2 t} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 6 \\ x_{2} \left (0\right ) &= 2 \\ x_{3} \left (0\right ) &= 3 \\ \end{align*}

1.004

12111

3759

\begin{align*} y^{\prime \prime }+2 y^{\prime }+17 y&=\frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}} \\ \end{align*}

1.005

12112

16923

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

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

1.005

12113

19875

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

1.005

12114

25246

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

Using Laplace transform method.

1.005

12115

26654

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

1.005

12116

2454

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

Series expansion around \(t=0\).

1.006

12117

5481

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

1.006

12118

8259

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

1.006

12119

9693

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

1.006

12120

10064

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

1.006

12121

15070

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

1.006

12122

19046

\begin{align*} x_{1}^{\prime }&=-4 x_{1}+x_{2}+3 x_{3}+3 t \\ x_{2}^{\prime }&=-2 x_{2} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \\ \end{align*}

1.006

12123

19757

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

1.006

12124

2455

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

Series expansion around \(t=0\).

1.007

12125

4071

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

Series expansion around \(x=0\).

1.007

12126

5464

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

1.007

12127

6243

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

1.007

12128

6611

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

1.007

12129

8521

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

Series expansion around \(x=0\).

1.007

12130

10048

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

1.007

12131

14060

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

1.007

12132

15779

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

1.007

12133

16654

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

1.007

12134

18241

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=10 \sin \left (x \right )+17 \sin \left (2 x \right ) \\ \end{align*}

1.007

12135

18271

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

1.007

12136

19619

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

Series expansion around \(x=3\).

1.007

12137

21691

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

Series expansion around \(x=0\).

1.007

12138

25338

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

Series expansion around \(t=0\).

1.007

12139

25539

\begin{align*} 4 y^{\prime \prime }+B y^{\prime }+16 y&=0 \\ \end{align*}

1.007

12140

19045

\begin{align*} x_{1}^{\prime }&=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\ x_{2}^{\prime }&=-x_{1}-2 x_{2}+x_{3}+t \\ x_{3}^{\prime }&=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \\ \end{align*}

1.008

12141

20945

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

With initial conditions

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

1.008

12142

813

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

1.009

12143

2450

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

Series expansion around \(t=0\).

1.009

12144

5772

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

1.009

12145

5899

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

1.009

12146

13027

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

1.009

12147

14648

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=18 \,{\mathrm e}^{-2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

1.009

12148

15466

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

1.009

12149

22174

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

Series expansion around \(x=1\).

1.009

12150

23105

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

1.009

12151

6762

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

1.010

12152

8582

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

Series expansion around \(x=0\).

1.010

12153

9569

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y&=0 \\ \end{align*}

1.010

12154

17867

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

1.010

12155

26553

\begin{align*} 7 y^{\prime \prime }-y^{\prime }&=14 x \\ \end{align*}

1.010

12156

3499

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

1.011

12157

5023

\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\ \end{align*}

1.011

12158

15007

\begin{align*} x^{\prime }&=-11 x-2 y \\ y^{\prime }&=13 x-9 y \\ \end{align*}

1.011

12159

15727

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

Using Laplace transform method.

1.011

12160

20535

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

1.011

12161

22847

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

Series expansion around \(x=0\).

1.011

12162

26058

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

1.011

12163

1995

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

Series expansion around \(x=0\).

1.012

12164

9585

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{2}+3\right ) y&=0 \\ \end{align*}

1.012

12165

16277

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

1.012

12166

16404

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

1.012

12167

20801

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

1.012

12168

22154

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

1.012

12169

3222

\begin{align*} 4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y&=0 \\ \end{align*}

1.013

12170

14660

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

1.013

12171

17489

\begin{align*} y^{\prime \prime }+2 y^{\prime }+50 y&={\mathrm e}^{-t} \csc \left (7 t \right ) \\ \end{align*}

1.013

12172

18645

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

1.013

12173

19005

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

1.013

12174

19526

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

1.013

12175

24701

\begin{align*} 4 y+y^{\prime \prime }&=12 \sin \left (x \right )+12 \sin \left (2 x \right ) \\ \end{align*}

1.013

12176

26646

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

1.013

12177

27394

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

1.013

12178

15324

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

With initial conditions

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

1.014

12179

18639

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

With initial conditions

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

1.014

12180

22782

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

1.014

12181

25376

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

With initial conditions

\begin{align*} y_{1} \left (0\right ) &= 2 \\ y_{2} \left (0\right ) &= 1 \\ y_{3} \left (0\right ) &= 2 \\ \end{align*}

1.014

12182

27342

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

1.014

12183

2081

\begin{align*} 3 x^{2} \left (x +3\right ) y^{\prime \prime }-x \left (15+x \right ) y^{\prime }-20 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.015

12184

13775

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

1.015

12185

14409

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

1.015

12186

14739

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

Series expansion around \(x=0\).

1.015

12187

24571

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

1.015

12188

3252

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

1.016

12189

7175

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

Series expansion around \(x=0\).

1.016

12190

8511

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

Series expansion around \(x=0\).

1.016

12191

13733

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

1.016

12192

1346

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

1.017

12193

2028

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

Series expansion around \(x=0\).

1.017

12194

6390

\begin{align*} a \,{\mathrm e}^{-1+y}+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

1.017

12195

10440

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

1.017

12196

10545

\begin{align*} x^{2} \left (10 x^{2}+x +5\right ) y^{\prime \prime }+x \left (48 x^{2}+3 x +4\right ) y^{\prime }+\left (36 x^{2}+x \right ) y&=0 \\ \end{align*}

1.017

12197

14787

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

1.017

12198

16065

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

1.017

12199

19994

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

1.017

12200

24729

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

1.017