2.3.218 Problems 21701 to 21800

Table 2.1009: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

21701

5744

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

6.066

21702

12923

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

6.067

21703

7856

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

6.070

21704

27388

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

6.070

21705

4076

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

6.073

21706

9651

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&={\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (-4+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

6.073

21707

20277

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

6.077

21708

12191

\begin{align*} y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\cos \left (x \right ) \ln \left (y\right )}{\sin \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \\ \end{align*}

6.078

21709

17331

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

6.079

21710

20222

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

6.079

21711

4333

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

6.082

21712

12253

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

6.082

21713

11506

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

6.083

21714

14910

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

6.083

21715

20736

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

6.083

21716

5282

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

6.086

21717

8320

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

6.086

21718

18024

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

6.086

21719

23165

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

6.086

21720

16320

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

6.089

21721

16146

\begin{align*} y^{\prime \prime }+y^{\prime }+8 y&=\left (1-\operatorname {Heaviside}\left (-4+t \right )\right ) \cos \left (-4+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

6.091

21722

26862

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

6.092

21723

19281

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

6.095

21724

6494

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

6.097

21725

13389

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

6.098

21726

5584

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

6.102

21727

15335

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

6.102

21728

24342

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

6.103

21729

21790

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

6.105

21730

4799

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

6.107

21731

11554

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

6.107

21732

13252

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

6.107

21733

16364

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

6.107

21734

24257

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

6.108

21735

2935

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

6.112

21736

19944

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

6.112

21737

27463

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

6.115

21738

4943

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

6.116

21739

20814

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

6.117

21740

5051

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

6.118

21741

17344

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

6.118

21742

27459

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

6.118

21743

11340

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

6.121

21744

22344

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

6.122

21745

26435

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

6.124

21746

27293

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

6.125

21747

6008

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

6.126

21748

14824

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=\left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

6.127

21749

8211

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

6.128

21750

9119

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

6.129

21751

19327

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

6.131

21752

19809

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

6.131

21753

12268

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

6.132

21754

4771

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

6.134

21755

12203

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

6.134

21756

9092

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

6.135

21757

12340

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

6.135

21758

5091

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

6.138

21759

5507

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

6.138

21760

9534

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

Series expansion around \(x=0\).

6.138

21761

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 y a^{2} x^{4}}{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*}

6.138

21762

17103

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

6.138

21763

3670

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

6.139

21764

8292

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

6.140

21765

11937

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

6.140

21766

18546

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

6.140

21767

1653

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

6.141

21768

22014

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

6.142

21769

24190

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

6.145

21770

17067

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

6.146

21771

4246

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

6.147

21772

12329

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

6.147

21773

4530

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \operatorname {Heaviside}\left (t -2\right ) t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

6.151

21774

17325

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

6.153

21775

7491

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

6.155

21776

14493

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

6.155

21777

16977

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

6.155

21778

12677

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

6.156

21779

26253

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

6.156

21780

12214

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

6.161

21781

26866

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

6.161

21782

4529

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 15 \\ y^{\prime }\left (0\right ) &= -6 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

6.162

21783

19268

\begin{align*} 3 \cos \left (3 x \right ) \cos \left (2 y\right )-2 \sin \left (3 x \right ) \sin \left (2 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{12}\right ) &= \frac {\pi }{8} \\ \end{align*}

6.162

21784

731

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

6.164

21785

7412

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

6.164

21786

22469

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

6.164

21787

22525

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

6.164

21788

6412

\begin{align*} b +a x y-\left (-12 x^{2}+k \,x^{-1+k}\right ) \left (y^{2}+3 y^{\prime }\right )+2 \left (-4 x^{3}+x^{k}\right ) \left (y y^{\prime }+y^{\prime \prime }-y^{3}\right )&=0 \\ \end{align*}

6.168

21789

4426

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

6.173

21790

6971

\begin{align*} \tan \left (\theta \right ) r^{\prime }-r&=\tan \left (\theta \right )^{2} \\ \end{align*}

6.174

21791

12198

\begin{align*} y^{\prime }&=\frac {2 y^{8}}{y^{5}+2 y^{6}+2 y^{2}+16 x y^{4}+32 y^{6} x^{2}+2+24 x y^{2}+96 x^{2} y^{4}+128 x^{3} y^{6}} \\ \end{align*}

6.174

21792

11374

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

6.176

21793

10436

\begin{align*} \cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \\ \end{align*}

6.179

21794

19360

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

6.180

21795

1670

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

6.185

21796

8460

\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y&=4 x \\ y \left (0\right ) &= 3 \\ \end{align*}

6.186

21797

23542

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=\ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \\ \end{align*}

6.187

21798

14899

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

6.193

21799

18105

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

6.194

21800

19668

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

6.194