2.3.72 Problems 7101 to 7200

Table 2.717: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

7101

18308

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

0.889

7102

19695

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

0.889

7103

24512

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

0.889

7104

2590

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

0.890

7105

9264

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

0.890

7106

15003

\begin{align*} x^{\prime }&=x+20 y \\ y^{\prime }&=40 x-19 y \\ \end{align*}

0.890

7107

19478

\begin{align*} y^{\prime \prime }-6 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 11 \\ \end{align*}

0.890

7108

20440

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

0.890

7109

20465

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

0.890

7110

995

\begin{align*} x_{1}^{\prime }&=-40 x_{1}-12 x_{2}+54 x_{3} \\ x_{2}^{\prime }&=35 x_{1}+13 x_{2}-46 x_{3} \\ x_{3}^{\prime }&=-25 x_{1}-7 x_{2}+34 x_{3} \\ \end{align*}

0.891

7111

1631

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

0.891

7112

2247

\begin{align*} y_{1}^{\prime }&=3 y_{1}+5 y_{2}+8 y_{3} \\ y_{2}^{\prime }&=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }&=-y_{1}-y_{2}-y_{3} \\ \end{align*}

0.891

7113

2648

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

Series expansion around \(t=0\).

0.891

7114

2730

\begin{align*} x_{1}^{\prime }&=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }&=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }&=-2 x_{1}+x_{2}-x_{3} \\ \end{align*}

0.891

7115

3766

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

0.891

7116

4041

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

Series expansion around \(x=0\).

0.891

7117

4071

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

Series expansion around \(x=0\).

0.891

7118

4184

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

Series expansion around \(x=0\).

0.891

7119

7295

\begin{align*} 5 y^{\prime \prime }+6 y^{\prime }+2 y&=x^{2}+6 x \\ \end{align*}

0.891

7120

14383

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

0.891

7121

14793

\begin{align*} x^{\prime }&=-2 x+7 y \\ y^{\prime }&=3 x+2 y \\ \end{align*}

With initial conditions

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

0.891

7122

15073

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

0.891

7123

15741

\(\left [\begin {array}{cc} -3 & -1 \\ 2 & -1 \end {array}\right ]\)

N/A

N/A

N/A

0.891

7124

15810

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

0.891

7125

16024

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

With initial conditions

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

0.891

7126

17299

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

0.891

7127

17486

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

0.891

7128

19692

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

0.891

7129

19843

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

0.891

7130

23358

\begin{align*} 5 y^{\prime \prime }+10 y^{\prime }+20 y&=0 \\ \end{align*}

0.891

7131

25259

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

0.891

7132

3822

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

0.892

7133

3841

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

0.892

7134

4376

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

0.892

7135

8003

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

0.892

7136

8940

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

0.892

7137

12741

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

0.892

7138

10944

\begin{align*} \left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y&=0 \\ \end{align*}

0.893

7139

11827

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

0.893

7140

13062

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

0.893

7141

14170

\begin{align*} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y&=0 \\ \end{align*}

0.893

7142

19756

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

0.893

7143

22483

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

0.893

7144

23520

\begin{align*} e i u^{\prime \prime \prime \prime }&=\sinh \left (x \right ) \\ \end{align*}

0.893

7145

25158

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{2 t} \\ \end{align*}

0.893

7146

8531

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

Series expansion around \(x=0\).

0.894

7147

9349

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

Series expansion around \(x=0\).

0.894

7148

16398

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

0.894

7149

16703

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

0.894

7150

26046

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

0.894

7151

26347

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

0.894

7152

13

\begin{align*} x^{\prime \prime }&=3 t \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 5 \\ \end{align*}

0.895

7153

6317

\begin{align*} y y^{\prime }+y^{\prime \prime }&=-12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right ) \\ \end{align*}

0.895

7154

6552

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

0.895

7155

9272

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

0.895

7156

18447

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

0.895

7157

20620

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

0.895

7158

23391

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

0.895

7159

2650

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

Series expansion around \(t=0\).

0.896

7160

20917

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

Using Laplace transform method.

0.896

7161

25257

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

0.896

7162

16947

\begin{align*} x^{\prime }&=4 x+3 y+5 \operatorname {Heaviside}\left (-2+t \right ) \\ y^{\prime }&=x+6 y+17 \operatorname {Heaviside}\left (-2+t \right ) \\ \end{align*}

With initial conditions

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

0.897

7163

21487

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

0.897

7164

834

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

0.898

7165

2101

\begin{align*} 4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 y^{\prime } x -\left (-x^{2}+35\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.898

7166

2448

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

Series expansion around \(t=0\).

0.898

7167

2802

\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*}

0.898

7168

3183

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

0.898

7169

4185

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

Series expansion around \(x=0\).

0.898

7170

7080

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

0.898

7171

7854

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

0.898

7172

9351

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

Series expansion around \(x=0\).

0.898

7173

15259

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

0.898

7174

16500

\begin{align*} y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\ \end{align*}

0.898

7175

21540

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=\frac {1}{1+{\mathrm e}^{-x}} \\ \end{align*}

0.898

7176

24473

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\ \end{align*}

0.898

7177

1729

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

0.899

7178

3142

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

0.899

7179

4183

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

Series expansion around \(x=0\).

0.899

7180

5798

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\cosh \left (x \right ) {\mathrm e}^{-3 x} \\ \end{align*}

0.899

7181

6478

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

0.899

7182

2394

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

0.900

7183

4036

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

Series expansion around \(x=0\).

0.900

7184

7276

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

0.900

7185

7288

\begin{align*} y^{\prime \prime }+8 y^{\prime }+25 y&=120 \sin \left (5 x \right ) \\ \end{align*}

0.900

7186

10460

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

0.900

7187

12676

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

0.900

7188

16540

\begin{align*} y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y&=0 \\ y \left (0\right ) &= 6 \\ y^{\prime }\left (0\right ) &= -28 \\ y^{\prime \prime }\left (0\right ) &= -102 \\ y^{\prime \prime \prime }\left (0\right ) &= 622 \\ \end{align*}

0.900

7189

16670

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=30 x \cos \left (2 x \right ) \\ \end{align*}

0.900

7190

16803

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

Using Laplace transform method.

0.900

7191

17723

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

Series expansion around \(x=0\).

0.900

7192

4569

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

0.901

7193

6102

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

0.901

7194

6544

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

0.901

7195

7285

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=100 \cos \left (4 x \right ) \\ \end{align*}

0.901

7196

9171

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

0.901

7197

11773

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

0.901

7198

16501

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

0.901

7199

19659

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

0.901

7200

919

\begin{align*} x^{\prime \prime }+6 x^{\prime }+13 x&=10 \sin \left (5 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.902