2.3.122 Problems 12101 to 12200

Table 2.787: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

12101

23986

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

0.957

12102

4506

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

0.958

12103

10198

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

0.958

12104

10306

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

0.958

12105

25413

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

0.958

12106

5723

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

0.959

12107

7311

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

0.959

12108

17686

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

0.959

12109

22203

\begin{align*} 2 x^{2} y^{\prime \prime }+7 x \left (x +1\right ) y^{\prime }-3 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.959

12110

8898

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

0.960

12111

9540

\begin{align*} y^{\prime \prime } x +y^{\prime }+10 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.960

12112

12458

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

0.960

12113

14681

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

0.960

12114

15162

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

0.960

12115

15403

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

0.960

12116

18566

\begin{align*} y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

0.960

12117

23789

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

0.960

12118

2027

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

0.961

12119

2189

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y&={\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right ) \\ \end{align*}

0.961

12120

6485

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

0.961

12121

14334

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

0.961

12122

16908

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

0.961

12123

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*}

0.961

12124

18926

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}
Using Laplace transform method.

0.961

12125

8975

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

0.962

12126

14279

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

0.962

12127

14812

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

0.962

12128

19886

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

0.962

12129

23594

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

0.962

12130

25219

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

0.962

12131

1749

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

0.963

12132

2082

\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*}
Series expansion around \(x=0\).

0.963

12133

7133

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

0.963

12134

9569

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

0.963

12135

17378

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

0.963

12136

20554

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

0.963

12137

20719

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

0.963

12138

7304

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

0.964

12139

9896

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

0.964

12140

13733

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

0.964

12141

14622

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

0.964

12142

14919

\begin{align*} z^{\prime \prime }-4 z^{\prime }+13 z&=0 \\ z \left (0\right ) &= 7 \\ z^{\prime }\left (0\right ) &= 42 \\ \end{align*}

0.964

12143

16944

\begin{align*} x^{\prime }&=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }&=x+6 y+2 \,{\mathrm e}^{3 t} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}

0.964

12144

17683

\begin{align*} y^{\prime \prime }+3 y^{\prime }-18 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.964

12145

16654

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

0.965

12146

20584

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

0.965

12147

22792

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

0.965

12148

6283

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

0.966

12149

8195

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

0.966

12150

16242

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

0.966

12151

17724

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

0.966

12152

23548

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

0.966

12153

35

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

0.967

12154

4138

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

0.967

12155

10180

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

0.967

12156

11565

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

0.967

12157

12978

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

0.967

12158

16384

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

0.967

12159

21676

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

0.967

12160

23707

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

0.967

12161

24411

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

0.967

12162

1949

\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*}
Series expansion around \(x=0\).

0.968

12163

3240

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

0.968

12164

4478

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

0.968

12165

6496

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

0.968

12166

8899

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

0.968

12167

12995

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

0.968

12168

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*}

0.968

12169

16410

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

0.968

12170

16891

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

0.968

12171

20635

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

0.968

12172

22927

\begin{align*} 2 x^{\prime }-x-y^{\prime }+y&=4 t \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{-t} \\ x^{\prime }+4 x-2 y^{\prime }-4 y&=2 t \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{-t} \\ \end{align*}

0.968

12173

25563

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&=0 \\ \end{align*}

0.968

12174

1835

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

0.969

12175

6891

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

0.969

12176

8321

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

0.969

12177

9564

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-25\right ) y&=0 \\ \end{align*}

0.969

12178

9939

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

0.969

12179

12949

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

0.969

12180

18723

\begin{align*} y^{\prime \prime }-t y&=\frac {1}{\pi } \\ \end{align*}

0.969

12181

21932

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

0.969

12182

22707

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

0.969

12183

1741

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

0.970

12184

2004

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

0.970

12185

2651

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

0.970

12186

4464

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

0.970

12187

9427

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

0.970

12188

10079

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

0.970

12189

16212

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

0.970

12190

17337

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

0.970

12191

18874

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

0.970

12192

20159

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

0.970

12193

20461

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

0.970

12194

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*}

0.970

12195

14122

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

0.971

12196

16406

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

0.971

12197

20647

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

0.971

12198

23420

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

0.971

12199

8363

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

0.972

12200

20556

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

0.972