2.3.142 Problems 14101 to 14200

Table 2.815: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14101

6236

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

2.747

14102

18562

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

2.747

14103

692

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

2.748

14104

20399

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

2.748

14105

21419

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

2.748

14106

4902

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

2.749

14107

3436

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

2.750

14108

4427

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

2.750

14109

4870

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

2.750

14110

9626

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

2.750

14111

19953

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

2.750

14112

24571

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

2.750

14113

25809

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

2.751

14114

763

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

2.752

14115

2332

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

2.753

14116

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*}

2.753

14117

5271

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

2.753

14118

14440

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

2.753

14119

15342

\begin{align*} 1+s^{2}-\sqrt {t}\, s^{\prime }&=0 \\ \end{align*}

2.753

14120

23896

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

2.753

14121

1001

\begin{align*} x_{1}^{\prime }&=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\ x_{2}^{\prime }&=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\ x_{3}^{\prime }&=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\ x_{4}^{\prime }&=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \\ \end{align*}

2.754

14122

131

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

2.755

14123

17175

\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

2.755

14124

19148

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

2.755

14125

21532

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 4 \\ \end{align*}

2.755

14126

4711

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

2.756

14127

15791

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

2.756

14128

5095

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

2.757

14129

5976

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

2.757

14130

10286

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

2.758

14131

11565

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

2.758

14132

4654

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

2.760

14133

20218

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

2.760

14134

23962

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

2.760

14135

17318

\begin{align*} 3 y+y^{\prime }&=-10 \sin \left (t \right ) \\ \end{align*}

2.762

14136

679

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

2.763

14137

4670

\begin{align*} y^{\prime }&=a \,x^{n -1}+b \,x^{2 n}+c y^{2} \\ \end{align*}

2.763

14138

7775

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

2.764

14139

15382

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

2.764

14140

524

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

2.765

14141

6441

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

2.765

14142

19957

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

2.765

14143

7535

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

2.766

14144

9089

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

2.766

14145

9519

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

2.766

14146

14050

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

2.766

14147

4974

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

2.767

14148

8388

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

2.767

14149

14263

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

2.767

14150

20687

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

2.767

14151

23152

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

2.767

14152

16

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

2.768

14153

3326

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

2.768

14154

4367

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

2.768

14155

17135

\begin{align*} y^{\prime }&=16 y-8 y^{2} \\ \end{align*}

2.768

14156

5817

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

2.770

14157

5196

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

2.771

14158

12342

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

2.771

14159

22584

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

2.771

14160

1498

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le t <10 \\ 0 & \operatorname {otherwise} \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

2.773

14161

7549

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

2.773

14162

17057

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

2.773

14163

21829

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

2.773

14164

14651

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=8 \,{\mathrm e}^{2 x}-5 \,{\mathrm e}^{3 x} \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

2.774

14165

17476

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

2.774

14166

19014

\begin{align*} x_{1}^{\prime }&=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\ x_{2}^{\prime }&=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\ x_{3}^{\prime }&=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\ x_{4}^{\prime }&=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \\ \end{align*}

2.774

14167

4437

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

2.775

14168

21413

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

2.775

14169

22562

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

2.775

14170

510

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

2.776

14171

6237

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

2.776

14172

4924

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

2.777

14173

13312

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

2.777

14174

14542

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

2.777

14175

6308

\begin{align*} y^{\prime \prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \\ \end{align*}

2.778

14176

7379

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

2.778

14177

20771

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

2.778

14178

5284

\begin{align*} x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y&=0 \\ \end{align*}

2.780

14179

21038

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

2.781

14180

24290

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

2.781

14181

3221

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +16 y&=0 \\ \end{align*}

2.782

14182

9500

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

2.782

14183

11321

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

2.782

14184

3536

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

2.783

14185

5537

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

2.783

14186

14518

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

2.783

14187

16270

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

2.783

14188

800

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

2.784

14189

17332

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

2.784

14190

3532

\begin{align*} y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \\ \end{align*}

2.785

14191

11425

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

2.785

14192

13706

\begin{align*} y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y&=0 \\ \end{align*}

2.785

14193

700

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

2.786

14194

18552

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

2.786

14195

22629

\begin{align*} 4 y^{\prime \prime }-25 y&=0 \\ \end{align*}

2.786

14196

728

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

2.787

14197

8305

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

2.787

14198

18289

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \\ y \left (\infty \right ) &= 0 \\ \end{align*}

2.787

14199

24841

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

2.787

14200

13708

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

2.788