2.3.92 Problems 9101 to 9200

Table 2.757: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

9101

27674

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

0.669

9102

15212

\begin{align*} y^{\prime \prime }+2 y^{\prime }+3 y&=9 t \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.670

9103

21749

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

0.670

9104

24090

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

Series expansion around \(x=0\).

0.670

9105

25369

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

With initial conditions

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

0.670

9106

27583

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

0.670

9107

2619

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

Series expansion around \(t=0\).

0.671

9108

2760

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

With initial conditions

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

0.671

9109

3261

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

0.671

9110

3749

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

0.671

9111

4005

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

Series expansion around \(x=0\).

0.671

9112

9772

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

0.671

9113

13728

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

0.671

9114

14953

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

0.671

9115

16611

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=25 \sin \left (6 x \right ) \\ \end{align*}

0.671

9116

16980

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

0.671

9117

18661

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

With initial conditions

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

0.671

9118

20850

\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=3 \,{\mathrm e}^{x} \\ \end{align*}

0.671

9119

20941

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

0.671

9120

21230

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

0.671

9121

22200

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

Series expansion around \(x=0\).

0.671

9122

23568

\begin{align*} x_{1}^{\prime }&=5 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }&=2 x_{1}+2 x_{2}-4 x_{3} \\ x_{3}^{\prime }&=2 x_{1}-4 x_{2}+2 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 ) &= 0 \\ \end{align*}

0.671

9123

24006

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

0.671

9124

25327

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

Series expansion around \(t=0\).

0.671

9125

26980

\begin{align*} y^{\prime \prime }-2 y^{\prime }-8 y&=10 \,{\mathrm e}^{-x}+8 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

0.671

9126

984

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

0.672

9127

3850

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

With initial conditions

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

0.672

9128

7699

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

0.672

9129

8017

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

0.672

9130

9343

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

0.672

9131

10001

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

0.672

9132

14415

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

0.672

9133

15219

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

Using Laplace transform method.

0.672

9134

21543

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

0.672

9135

22305

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

0.672

9136

25127

\begin{align*} y^{\prime \prime }-5 y^{\prime }-6 y&={\mathrm e}^{3 t} \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.672

9137

26566

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

0.672

9138

1031

\begin{align*} x_{1}^{\prime }&=28 x_{1}+50 x_{2}+100 x_{3} \\ x_{2}^{\prime }&=15 x_{1}+33 x_{2}+60 x_{3} \\ x_{3}^{\prime }&=-15 x_{1}-30 x_{2}-57 x_{3} \\ \end{align*}

0.673

9139

3185

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

0.673

9140

11812

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

0.673

9141

14310

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

0.673

9142

14817

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 \,{\mathrm e}^{-t} \sin \left (3 t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}

Using Laplace transform method.

0.673

9143

17461

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=3 t \\ y \left (0\right ) &= {\frac {23}{12}} \\ y^{\prime }\left (0\right ) &= -{\frac {3}{2}} \\ \end{align*}

0.673

9144

17770

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

0.673

9145

19771

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

0.673

9146

20163

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

0.673

9147

20855

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

0.673

9148

21242

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

0.673

9149

23492

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

0.673

9150

24625

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=20-3 x \,{\mathrm e}^{2 x} \\ \end{align*}

0.673

9151

127

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

0.674

9152

1030

\begin{align*} x_{1}^{\prime }&=39 x_{1}+8 x_{2}-16 x_{3} \\ x_{2}^{\prime }&=-36 x_{1}-5 x_{2}+16 x_{3} \\ x_{3}^{\prime }&=72 x_{1}+16 x_{2}-29 x_{3} \\ \end{align*}

0.674

9153

1360

\begin{align*} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5}&=\cos \left (t \right ) \\ u \left (0\right ) &= 2 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.674

9154

3239

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

0.674

9155

7767

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

0.674

9156

8385

\begin{align*} y^{\prime }&=\left (-1+y\right )^{2} \\ y \left (0\right ) &= {\frac {101}{100}} \\ \end{align*}

0.674

9157

9979

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

0.674

9158

12978

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

0.674

9159

17033

\begin{align*} y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\ y \left (0\right ) &= 0 \\ \end{align*}

0.674

9160

18650

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

0.674

9161

18892

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

Using Laplace transform method.

0.674

9162

19873

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

0.674

9163

22891

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

0.674

9164

23937

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

0.674

9165

24464

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

0.674

9166

1414

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

0.675

9167

2403

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

0.675

9168

2766

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

0.675

9169

6704

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

0.675

9170

9061

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

0.675

9171

10043

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

0.675

9172

18655

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

0.675

9173

18670

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

With initial conditions

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

0.675

9174

18784

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}

0.675

9175

20447

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

0.675

9176

21494

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

0.675

9177

21623

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

0.675

9178

21963

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

0.675

9179

22748

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=2 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{-5 x} \\ \end{align*}

0.675

9180

27103

\(\left [\begin {array}{cccc} 5 & 1 & 0 & 9 \\ 0 & 1 & 0 & 9 \\ 0 & 0 & 0 & 9 \\ 0 & 0 & 0 & 0 \end {array}\right ]\)

N/A

N/A

N/A

0.675

9181

4368

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

0.676

9182

11749

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

0.676

9183

15000

\begin{align*} x^{\prime }&=8 x+14 y \\ y^{\prime }&=7 x+y \\ \end{align*}

0.676

9184

15724

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

Using Laplace transform method.

0.676

9185

346

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

0.677

9186

10137

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

0.677

9187

14383

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

0.677

9188

15735

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

With initial conditions

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

0.677

9189

16626

\begin{align*} y^{\prime \prime }+9 y&=39 x \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.677

9190

20552

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

0.677

9191

22920

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

With initial conditions

\begin{align*} x \left (0\right ) &= 0 \\ y \left (0\right ) &= -10 \\ \end{align*}

0.677

9192

23529

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=\frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \\ \end{align*}

0.677

9193

23723

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

Series expansion around \(x=0\).

0.677

9194

24741

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

0.677

9195

25953

\begin{align*} y^{\prime \prime }-9 y&={\mathrm e}^{3 x} \\ \end{align*}

0.677

9196

3839

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

0.678

9197

3885

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=x_{2}-8 x_{3} \\ x_{3}^{\prime }&=2 x_{2}-7 x_{3} \\ \end{align*}

0.678

9198

6646

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

0.678

9199

7034

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

0.678

9200

7626

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

Series expansion around \(t=0\).

0.678