2.3.92 Problems 9101 to 9200

Table 2.715: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9101

24759

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

0.947

9102

6339

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

0.948

9103

10207

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

0.948

9104

13297

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

0.948

9105

19042

\begin{align*} x_{1}^{\prime }&=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+\sin \left (t \right ) \\ \end{align*}

0.948

9106

4431

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

0.949

9107

9677

\begin{align*} x^{\prime }&=2 x-7 y \\ y^{\prime }&=5 x+10 y+4 z \\ z^{\prime }&=5 y+2 z \\ \end{align*}

0.949

9108

10679

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

0.949

9109

18996

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

0.950

9110

21742

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

0.950

9111

1968

\begin{align*} 2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.951

9112

6391

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

0.951

9113

10339

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

0.951

9114

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*}

0.951

9115

23273

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

0.951

9116

95

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

0.952

9117

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*}

0.952

9118

14025

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

0.952

9119

16243

\begin{align*} y^{\prime }&={\mathrm e}^{-y}+1 \\ \end{align*}

0.952

9120

16905

\begin{align*} \left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.952

9121

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*}

0.952

9122

1036

\begin{align*} x_{1}^{\prime }&=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }&=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }&=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }&=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \\ \end{align*}

0.953

9123

10599

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

0.953

9124

16841

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

0.953

9125

19701

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

0.953

9126

7225

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

0.954

9127

8132

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

0.954

9128

10687

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

0.954

9129

11129

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

0.954

9130

15005

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

0.954

9131

16911

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

0.954

9132

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*}

0.954

9133

17420

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

0.954

9134

21629

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

0.954

9135

16880

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

0.955

9136

21634

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

0.955

9137

3371

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

0.957

9138

5880

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

0.957

9139

8134

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

0.957

9140

20564

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

0.957

9141

8840

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

0.958

9142

9267

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

0.958

9143

20908

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

0.958

9144

21446

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

0.958

9145

1185

\begin{align*} y^{\prime }&=-1+{\mathrm e}^{-y} \\ \end{align*}

0.959

9146

23032

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

0.959

9147

11035

\begin{align*} 4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y&=0 \\ \end{align*}

0.960

9148

12982

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

0.960

9149

24724

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

0.960

9150

219

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

0.961

9151

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 \(x=0\).

0.961

9152

9555

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

0.961

9153

15243

\begin{align*} y^{\prime \prime }+4 y^{\prime }+29 y&=5 \delta \left (t -\pi \right )-5 \delta \left (t -2 \pi \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.961

9154

16872

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

0.961

9155

17788

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

0.961

9156

1952

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

0.962

9157

11088

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

0.962

9158

24101

\begin{align*} x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

0.962

9159

8415

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

0.963

9160

9393

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

0.963

9161

10538

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

0.963

9162

11217

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

0.963

9163

11389

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

0.963

9164

16155

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

0.963

9165

3393

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

0.964

9166

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*}

0.964

9167

6810

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

0.964

9168

10765

\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ \end{align*}

0.964

9169

11021

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

0.964

9170

11027

\begin{align*} 9 x^{2} y^{\prime \prime }-3 x \left (-2 x^{2}+7\right ) y^{\prime }+\left (2 x^{2}+25\right ) y&=0 \\ \end{align*}

0.964

9171

22726

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

0.964

9172

25030

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

0.964

9173

25684

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

0.964

9174

5843

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

0.966

9175

2354

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

0.967

9176

4295

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

0.967

9177

6422

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

0.967

9178

7069

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

0.967

9179

11166

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

0.967

9180

11215

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

0.967

9181

11288

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

0.967

9182

13022

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

0.967

9183

14201

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

0.967

9184

18116

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

0.967

9185

18787

\begin{align*} 6 y^{\prime \prime }-5 y^{\prime }+y&=0 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.967

9186

22286

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

0.967

9187

24433

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

0.967

9188

1239

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

0.968

9189

14428

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

0.968

9190

15794

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

0.968

9191

7910

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

0.969

9192

1184

\begin{align*} y^{\prime }&=-1+{\mathrm e}^{y} \\ \end{align*}

0.970

9193

4011

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

0.970

9194

4058

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

0.970

9195

10666

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

0.970

9196

11292

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

0.970

9197

22134

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

0.970

9198

22942

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

0.970

9199

23687

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

0.970

9200

9861

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

0.971