2.3.142 Problems 14101 to 14200

Table 2.815: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14101

3351

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

0.969

14102

9413

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

0.969

14103

12284

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

0.969

14104

25741

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

0.969

14105

3395

\begin{align*} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \\ \end{align*}
Series expansion around \(x=0\).

0.970

14106

8332

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

0.970

14107

9865

\begin{align*} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x -\left (x +1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.970

14108

9969

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

0.970

14109

10433

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

0.970

14110

18108

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

0.970

14111

21741

\begin{align*} x^{\prime }&=7 x-y+6 z \\ y^{\prime }&=-10 x+4 y-12 z \\ z^{\prime }&=-2 x+y-z \\ \end{align*}

0.970

14112

22022

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

0.970

14113

25740

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

0.970

14114

990

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{3} \\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 17 \\ \end{align*}

0.971

14115

6401

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

0.971

14116

9654

\begin{align*} x^{\prime }&=3 x-5 y \\ y^{\prime }&=4 x+8 y \\ \end{align*}

0.971

14117

9947

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

0.971

14118

13720

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

0.971

14119

13874

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

0.971

14120

23234

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

0.971

14121

9626

\begin{align*} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.972

14122

9821

\begin{align*} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\ \end{align*}

0.972

14123

5411

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

0.973

14124

8241

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

0.973

14125

8283

\begin{align*} y^{\prime \prime }+9 y&=5 \\ \end{align*}

0.973

14126

13685

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

0.973

14127

13691

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

0.973

14128

13786

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

0.973

14129

14300

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

0.973

14130

15655

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

0.973

14131

18337

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

0.973

14132

20556

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

0.973

14133

20843

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

0.973

14134

646

\begin{align*} x_{1}^{\prime }&=3 x_{1}+x_{3} \\ x_{2}^{\prime }&=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }&=-9 x_{1}+4 x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 17 \\ \end{align*}

0.974

14135

2103

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.974

14136

3256

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

0.974

14137

8208

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

0.974

14138

9964

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

0.974

14139

25765

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

0.974

14140

3252

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

0.975

14141

3311

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

0.975

14142

20501

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

0.975

14143

21672

\begin{align*} 8 x^{2} y^{\prime \prime }+10 y^{\prime } x +\left (x -1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.975

14144

3300

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

0.976

14145

22980

\begin{align*} y^{\prime }-6 y&={\mathrm e}^{6 t} \\ y \left (0\right ) &= 0 \\ \end{align*}

0.976

14146

8366

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

0.977

14147

9415

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

0.977

14148

9870

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

0.977

14149

11760

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

0.977

14150

12299

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

0.977

14151

12326

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

0.977

14152

13945

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

0.977

14153

15005

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

0.977

14154

16259

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

0.977

14155

17998

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

0.977

14156

2662

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

0.978

14157

5940

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

0.978

14158

21244

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

0.978

14159

24772

\begin{align*} 2 y^{\prime }+2 y+w^{\prime }-w&=x +1 \\ y^{\prime }+3 y+w^{\prime }+w&=4 x +14 \\ \end{align*}

0.978

14160

4752

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

0.979

14161

15163

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

0.979

14162

18644

\begin{align*} x^{\prime }&=-2 x+y-11 \\ y^{\prime }&=-5 x+4 y-35 \\ \end{align*}

0.979

14163

20947

\begin{align*} x^{\prime }&=2 x-y+\cos \left (t \right ) \\ y^{\prime }&=5 x-2 y+\sin \left (t \right ) \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= 1 \\ \end{align*}

0.979

14164

22505

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

0.979

14165

25212

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

0.979

14166

1330

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

0.980

14167

5215

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

0.980

14168

8217

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

0.980

14169

8827

\begin{align*} \left (\phi ^{\prime }-\frac {\phi ^{2}}{2}\right ) \sin \left (\theta \right )^{2}-\phi \sin \left (\theta \right ) \cos \left (\theta \right )&=\frac {\cos \left (2 \theta \right )}{2}+1 \\ \end{align*}

0.980

14170

9948

\begin{align*} 2 \left (x +5\right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.980

14171

12119

\begin{align*} y^{\prime }&=\frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 \sqrt {x}\, y+4 x^{6}+40 x^{{7}/{2}}+100 x}{25 x} \\ \end{align*}

0.980

14172

13787

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

0.980

14173

16157

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

0.980

14174

18084

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

0.980

14175

5472

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

0.981

14176

14434

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

0.981

14177

22499

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

0.981

14178

3314

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

0.982

14179

8988

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

0.982

14180

3310

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

0.983

14181

5473

\begin{align*} x {y^{\prime }}^{2}-3 y^{\prime } y+9 x^{2}&=0 \\ \end{align*}

0.983

14182

19001

\begin{align*} x_{1}^{\prime }&=x_{1}+8 x_{2}+5 x_{3}+3 x_{4} \\ x_{2}^{\prime }&=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4} \\ x_{4}^{\prime }&=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4} \\ \end{align*}

0.983

14183

20640

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

0.983

14184

23322

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

0.983

14185

231

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

0.984

14186

2290

\begin{align*} y_{1}^{\prime }&=-3 y_{1}+3 y_{2}+y_{3} \\ y_{2}^{\prime }&=y_{1}-5 y_{2}-3 y_{3} \\ y_{3}^{\prime }&=-3 y_{1}+7 y_{2}+3 y_{3} \\ \end{align*}

0.984

14187

4597

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

0.984

14188

5388

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

0.984

14189

7128

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

0.984

14190

13900

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

0.984

14191

18119

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

0.984

14192

20175

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

0.984

14193

19700

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

0.985

14194

25223

\begin{align*} 2 t^{2} y^{\prime \prime }-5 t y^{\prime }+3 y&=0 \\ \end{align*}

0.985

14195

20981

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

0.986

14196

271

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

0.987

14197

3397

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

0.987

14198

5548

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

0.987

14199

5861

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

0.987

14200

9776

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

0.987