2.3.167 Problems 16601 to 16700

Table 2.865: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

16601

13323

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

4.127

16602

19689

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

4.129

16603

10237

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

4.130

16604

18872

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

4.130

16605

5213

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

4.131

16606

6028

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

4.133

16607

12381

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

4.133

16608

5272

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

4.135

16609

13693

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

4.137

16610

17469

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

4.137

16611

5330

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

4.138

16612

15461

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

4.138

16613

22700

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

4.139

16614

12335

\begin{align*} y^{\prime \prime }+a \,x^{-1+q} y^{\prime }+b \,x^{q -2} y&=0 \\ \end{align*}

4.140

16615

16368

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

4.140

16616

12230

\begin{align*} y^{\prime }&=-\frac {a x}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a \,x^{3} b}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 a \,x^{2} y^{2}}{4}+\frac {3 b x y^{2}}{2}+\frac {3 a^{2} x^{4} y}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 b^{2} x^{2} y}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 b^{2} x^{4} a}{16}+\frac {b^{3} x^{3}}{8} \\ \end{align*}

4.141

16617

14514

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

4.141

16618

8350

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

4.142

16619

12244

\begin{align*} y^{\prime }&=-\frac {8 x \left (-1+a \right ) \left (1+a \right )}{8+x^{6}-8 y+2 x^{4}-a^{2} y^{6}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-8 y^{2} a^{2} x^{2}+2 y^{4}+3 x^{2} y^{4}-2 y^{4} a^{2}-6 a^{2} x^{4}-8 a^{2}+4 y^{2} x^{2}+y^{6}+3 y^{2} x^{4}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+4 a^{4} y^{2} x^{2}-4 a^{2} x^{6}-6 y^{4} a^{2} x^{2}-2 a^{6} x^{4}+6 a^{4} x^{4}} \\ \end{align*}

4.142

16620

4418

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

4.143

16621

4847

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

4.143

16622

6159

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

4.144

16623

22103

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

4.144

16624

23923

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

4.144

16625

13651

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

4.146

16626

13660

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

4.146

16627

7483

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

4.147

16628

11495

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

4.147

16629

13736

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

4.148

16630

16385

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\ \end{align*}

4.150

16631

4721

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

4.151

16632

6009

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

4.151

16633

7476

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

4.151

16634

11601

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

4.151

16635

14180

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

4.151

16636

19385

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

4.151

16637

4825

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

4.153

16638

20500

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

4.153

16639

14357

\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x&=1-\operatorname {Heaviside}\left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

4.154

16640

15350

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

4.154

16641

24244

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

4.154

16642

14421

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

4.155

16643

24188

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

4.155

16644

2930

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

4.156

16645

5214

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

4.156

16646

7071

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

4.156

16647

18486

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

4.157

16648

22677

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

4.157

16649

2857

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

4.158

16650

25189

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

4.158

16651

25736

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

4.158

16652

23848

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

4.159

16653

14638

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

4.160

16654

1329

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

4.162

16655

17074

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

4.162

16656

24196

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

4.162

16657

15840

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

4.164

16658

819

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

4.165

16659

794

\begin{align*} 9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\ \end{align*}

4.166

16660

12538

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

4.166

16661

13700

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

4.166

16662

18389

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

4.166

16663

4926

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

4.170

16664

8657

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

4.171

16665

17156

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

4.172

16666

108

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

4.173

16667

163

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

4.174

16668

15792

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

4.174

16669

25197

\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } t +6 y&=2 t \\ y \left (0\right ) &= a \\ y^{\prime }\left (0\right ) &= b \\ \end{align*}

4.174

16670

14538

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+1} \\ y \left (\sqrt {15}\right ) &= 2 \\ \end{align*}

4.175

16671

23297

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

4.175

16672

20451

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

4.177

16673

25199

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

4.177

16674

20204

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

4.180

16675

1818

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

4.181

16676

823

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

4.182

16677

1349

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

4.184

16678

8689

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

4.184

16679

9569

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

4.185

16680

13698

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

4.185

16681

17166

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

4.185

16682

15508

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

4.186

16683

7145

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

4.187

16684

18292

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

4.189

16685

1702

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

4.190

16686

11763

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

4.191

16687

697

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

4.192

16688

14455

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

4.194

16689

20638

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

4.194

16690

3058

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

4.195

16691

19323

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

4.195

16692

24885

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

4.195

16693

3226

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

4.196

16694

11500

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

4.196

16695

5295

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

4.197

16696

7467

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

4.197

16697

22377

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

4.197

16698

7499

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

4.198

16699

17473

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

4.198

16700

14700

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

4.199