2.3.22 Problems 2101 to 2200

Table 2.575: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

2101

11297

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

0.128

2102

12720

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

0.128

2103

13998

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

0.128

2104

15194

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+13 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.128

2105

16466

\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&={\mathrm e}^{3 x} \sin \left (x \right ) \\ \end{align*}

0.128

2106

17375

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

0.128

2107

17734

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

0.128

2108

18459

\begin{align*} 2 x^{\prime }+6 x&=t \,{\mathrm e}^{-3 t} \\ x \left (0\right ) &= -{\frac {1}{2}} \\ \end{align*}
Using Laplace transform method.

0.128

2109

18750

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

0.128

2110

20164

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

0.128

2111

20707

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

0.128

2112

21960

\begin{align*} b^{\left (7\right )}&=3 p \\ \end{align*}

0.128

2113

22231

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

0.128

2114

22246

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

0.128

2115

24861

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

0.128

2116

343

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

0.129

2117

415

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

0.129

2118

3153

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

0.129

2119

4114

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

0.129

2120

4468

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime }&=7+x \\ \end{align*}

0.129

2121

7822

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

0.129

2122

9308

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \\ \end{align*}

0.129

2123

11078

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

0.129

2124

12812

\begin{align*} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\ \end{align*}

0.129

2125

12918

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

0.129

2126

14339

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

0.129

2127

14353

\begin{align*} x^{\prime \prime }-x^{\prime }-6 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

0.129

2128

14709

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 y^{\prime } x -8 y&=0 \\ \end{align*}

0.129

2129

14710

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 y^{\prime } x +18 y&=0 \\ \end{align*}

0.129

2130

14950

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

0.129

2131

15096

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

0.129

2132

15189

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 3 \\ \end{align*}
Using Laplace transform method.

0.129

2133

16814

\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.129

2134

19408

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

0.129

2135

22794

\begin{align*} i^{\prime \prime \prime \prime }+9 i^{\prime \prime }&=20 \,{\mathrm e}^{-t} \\ i \left (0\right ) &= 0 \\ i^{\prime }\left (0\right ) &= 0 \\ \end{align*}

0.129

2136

23642

\begin{align*} y^{\prime \prime }+9 y&={\mathrm e}^{t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.129

2137

23654

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=3 \,{\mathrm e}^{-2 t}-6 \,{\mathrm e}^{-5 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.129

2138

255

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\ y \left (1\right ) &= 6 \\ y^{\prime }\left (1\right ) &= 14 \\ y^{\prime \prime }\left (1\right ) &= 22 \\ \end{align*}

0.130

2139

2725

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

0.130

2140

3941

\begin{align*} y^{\prime \prime }-y&=12 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.130

2141

11240

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

0.130

2142

14956

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

0.130

2143

17248

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

0.130

2144

17563

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

0.130

2145

18221

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

0.130

2146

18313

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

0.130

2147

20610

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

0.130

2148

22479

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

0.130

2149

1325

\begin{align*} x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y&=0 \\ \end{align*}

0.131

2150

2140

\begin{align*} 4 y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+19 y^{\prime \prime }+32 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -3 \\ y^{\prime \prime }\left (0\right ) &= -{\frac {7}{2}} \\ y^{\prime \prime \prime }\left (0\right ) &= {\frac {31}{4}} \\ \end{align*}

0.131

2151

3691

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

0.131

2152

4517

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t} \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

0.131

2153

7191

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

0.131

2154

14708

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

0.131

2155

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*}

0.131

2156

16580

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y&=0 \\ \end{align*}

0.131

2157

16795

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

0.131

2158

17364

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=0 \\ \end{align*}

0.131

2159

18984

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

0.131

2160

20084

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

0.131

2161

22691

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

0.131

2162

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*}

0.131

2163

23663

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

0.131

2164

24783

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

0.131

2165

345

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

0.132

2166

359

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

0.132

2167

564

\begin{align*} x^{\prime \prime }+4 x&=\delta \left (t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.132

2168

2206

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&={\mathrm e}^{2 x} \left (10+3 x \right ) \\ \end{align*}

0.132

2169

2672

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

0.132

2170

3938

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=10 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}
Using Laplace transform method.

0.132

2171

4470

\begin{align*} y^{\prime \prime \prime \prime }+16 y&=64 \cos \left (2 x \right ) \\ \end{align*}

0.132

2172

4489

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \sin \left (2 x \right ) \\ \end{align*}

0.132

2173

9614

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=t^{3} {\mathrm e}^{2 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.132

2174

10355

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

0.132

2175

14629

\begin{align*} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y&=3 x^{3}-8 x \\ \end{align*}

0.132

2176

15225

\begin{align*} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

0.132

2177

16149

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

0.132

2178

17218

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

0.132

2179

18180

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}

0.132

2180

18214

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

0.132

2181

20988

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

0.132

2182

25509

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

0.132

2183

256

\begin{align*} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 y^{\prime } x -4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 5 \\ y^{\prime \prime }\left (1\right ) &= -11 \\ \end{align*}

0.133

2184

356

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

0.133

2185

7820

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

0.133

2186

13626

\begin{align*} \left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+B y x +\left (A b +k \right ) y+B b x +b k \\ \end{align*}

0.133

2187

20579

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

0.133

2188

20806

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \\ \end{align*}

0.133

2189

22261

\begin{align*} y^{\prime }-z&=0 \\ y-z^{\prime }&=0 \\ \end{align*}
With initial conditions
\begin{align*} y \left (0\right ) &= 1 \\ z \left (0\right ) &= 1 \\ \end{align*}

0.133

2190

25061

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

0.133

2191

9022

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

0.134

2192

11208

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

0.134

2193

14830

\begin{align*} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \\ \end{align*}

0.134

2194

14844

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

0.134

2195

17363

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}

0.134

2196

18181

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

0.134

2197

18905

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

0.134

2198

23481

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

0.134

2199

2316

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

0.135

2200

4488

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=15 \sin \left (2 x \right ) \\ \end{align*}

0.135