2.3.152 Problems 15101 to 15200

Table 2.835: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15101

8119

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

1.195

15102

21592

\begin{align*} 2 x^{\prime }-3 x-2 y^{\prime }&=t \\ 2 x^{\prime }+3 x+2 y^{\prime }+8 y&=2 \\ \end{align*}

1.195

15103

5652

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

1.196

15104

9418

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

1.196

15105

22869

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

1.196

15106

5668

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

1.197

15107

8064

\begin{align*} x^{\prime }+x+2 y^{\prime }+7 y&={\mathrm e}^{t}+2 \\ -2 x+y^{\prime }+3 y&={\mathrm e}^{t}-1 \\ \end{align*}

1.197

15108

122

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

1.198

15109

455

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

1.198

15110

4773

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

1.198

15111

5356

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

1.198

15112

17488

\begin{align*} y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \\ \end{align*}

1.198

15113

23193

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

1.198

15114

9938

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

1.199

15115

25362

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

1.199

15116

104

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

1.200

15117

2780

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

1.200

15118

5748

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

1.200

15119

15721

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

1.200

15120

16602

\begin{align*} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x \\ \end{align*}

1.200

15121

20203

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

1.201

15122

23137

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

1.201

15123

9770

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

1.202

15124

4579

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }&=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }&=2 x_{1}-x_{2} \\ \end{align*}

1.203

15125

14834

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

1.203

15126

19664

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

1.203

15127

6005

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

1.204

15128

8640

\begin{align*} y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0<t <\pi \\ 0 & \pi <t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}
Using Laplace transform method.

1.204

15129

12292

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

1.204

15130

12400

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

1.204

15131

16416

\begin{align*} y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\ y \left (1\right ) &= 8 \\ y^{\prime }\left (1\right ) &= -3 \\ \end{align*}

1.204

15132

25730

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

1.204

15133

12354

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

1.205

15134

16378

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

1.205

15135

18844

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

1.205

15136

20110

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

1.205

15137

5061

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

1.206

15138

3727

\begin{align*} y^{\prime \prime }+\omega ^{2} y&=\frac {F_{0} \cos \left (\omega t \right )}{m} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.207

15139

8297

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

1.207

15140

8860

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

1.207

15141

11677

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

1.207

15142

12946

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

1.207

15143

21129

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

1.207

15144

22318

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

1.207

15145

3578

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

1.208

15146

13209

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

1.208

15147

22946

\begin{align*} x^{\prime }+4 x+2 y-z&=12 \,{\mathrm e}^{t} \\ y^{\prime }-2 x-5 y+3 z&=0 \\ z^{\prime }+4 x+z&=30 \,{\mathrm e}^{-t} \\ \end{align*}

1.208

15148

2193

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+26 y^{\prime \prime }-40 y^{\prime }+25 y&={\mathrm e}^{2 x} \left (3 \cos \left (x \right )-\left (1+3 x \right ) \sin \left (x \right )\right ) \\ \end{align*}

1.210

15149

668

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

1.211

15150

3595

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

1.211

15151

13759

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

1.211

15152

16305

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

1.211

15153

21956

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

1.211

15154

22456

\begin{align*} i^{\prime }+2 i&=10 \,{\mathrm e}^{-2 t} \\ i \left (0\right ) &= 0 \\ \end{align*}

1.211

15155

25462

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

1.211

15156

10149

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

1.212

15157

22900

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

1.212

15158

168

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

1.213

15159

8766

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

1.213

15160

9214

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

1.213

15161

13751

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

1.213

15162

15604

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

1.213

15163

18015

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

1.213

15164

216

\begin{align*} y^{\prime \prime }-9 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 15 \\ \end{align*}

1.214

15165

2409

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

1.214

15166

3399

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

1.214

15167

5669

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

1.214

15168

13722

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

1.214

15169

8449

\begin{align*} T^{\prime }&=k \left (T-T_{m} \right ) \\ T \left (0\right ) &= T_{0} \\ \end{align*}

1.215

15170

18209

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

1.215

15171

23032

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

1.215

15172

16419

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

1.216

15173

17864

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

1.216

15174

8298

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

1.217

15175

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*}

1.217

15176

25235

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

1.217

15177

12307

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

1.218

15178

21961

\begin{align*} {b^{\prime }}^{7}&=3 p \\ \end{align*}

1.218

15179

10534

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

1.219

15180

19195

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

1.219

15181

22739

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

1.219

15182

2067

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

1.220

15183

2302

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

1.220

15184

11612

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

1.220

15185

20411

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

1.220

15186

21903

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

1.220

15187

26

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

1.221

15188

3514

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

1.221

15189

4215

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

1.221

15190

18290

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

1.221

15191

19568

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

1.221

15192

24351

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

1.221

15193

23151

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

1.222

15194

5716

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

1.223

15195

8456

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

1.223

15196

9792

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

1.223

15197

21702

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

1.223

15198

25612

\begin{align*} y^{\prime }-a y&=f \left (t \right ) \\ \end{align*}

1.223

15199

6334

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

1.224

15200

16338

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

1.224