2.3.221 Problems 22001 to 22100

Table 2.1015: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22001

11457

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

6.523

22002

9936

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

Series expansion around \(x=0\).

6.529

22003

9924

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

Series expansion around \(x=0\).

6.530

22004

14056

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

6.531

22005

8369

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

6.533

22006

20485

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

6.533

22007

8400

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{\sqrt {x}}}{y} \\ y \left (1\right ) &= 4 \\ \end{align*}

6.534

22008

14527

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

6.536

22009

17125

\begin{align*} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

6.536

22010

14530

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

6.537

22011

20303

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

6.537

22012

27436

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

6.539

22013

21338

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

6.542

22014

24374

\begin{align*} 4 y^{2}+10 y x -4 y+8+x \left (2 x +2 y-1\right ) y^{\prime }&=0 \\ \end{align*}

6.542

22015

117

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

6.546

22016

17039

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

6.548

22017

12218

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

6.549

22018

22436

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

6.549

22019

12110

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

6.550

22020

5426

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

6.551

22021

9927

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

Series expansion around \(x=0\).

6.553

22022

13025

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

6.553

22023

11725

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

6.555

22024

11351

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

6.557

22025

18550

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

6.557

22026

10454

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

Series expansion around \(x=0\).

6.558

22027

11375

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

6.558

22028

9999

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

6.559

22029

8167

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

6.560

22030

9387

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

Series expansion around \(x=0\).

6.563

22031

2478

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

6.567

22032

186

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

6.569

22033

2916

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

6.569

22034

11593

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

6.569

22035

13959

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

6.572

22036

22451

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

6.572

22037

18930

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

6.574

22038

4259

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

6.575

22039

6519

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

6.576

22040

9365

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

6.579

22041

9531

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

Series expansion around \(x=0\).

6.580

22042

12114

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

6.582

22043

15135

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

6.583

22044

24401

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

6.583

22045

12301

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

6.586

22046

19898

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

6.586

22047

24959

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

6.586

22048

25822

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

6.587

22049

22528

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

6.590

22050

12381

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

6.592

22051

25736

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

6.597

22052

9143

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

6.598

22053

4790

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

6.603

22054

8437

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

6.603

22055

24230

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

6.603

22056

11422

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

6.607

22057

12228

\begin{align*} y^{\prime }&=-\frac {216 y}{-216 y^{4}-252 y^{3}-396 y^{2}-216 y+36 x^{2}-72 y x +60 y^{5}-36 x y^{3}-72 x y^{2}-24 x y^{4}+4 y^{8}+12 y^{7}+33 y^{6}} \\ \end{align*}

6.607

22058

4199

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

6.611

22059

6239

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

6.613

22060

12207

\begin{align*} y^{\prime }&=-\frac {x \left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y-2 \,{\mathrm e}^{-2 x^{2}} x^{4}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 y^{2}-8 \,{\mathrm e}^{-x^{2}}-8\right )}{8} \\ \end{align*}

6.614

22061

5853

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

6.615

22062

19918

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

6.616

22063

22032

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

6.616

22064

11851

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

6.617

22065

15116

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

6.618

22066

22538

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

6.621

22067

6458

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

6.622

22068

23209

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

6.624

22069

26273

\begin{align*} 2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\ \end{align*}

6.624

22070

6270

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

6.625

22071

15094

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

6.625

22072

11789

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

6.627

22073

15610

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

6.630

22074

19738

\begin{align*} y^{\prime \prime }&=\frac {m \sqrt {1+{y^{\prime }}^{2}}}{k} \\ \end{align*}

6.631

22075

8406

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

6.635

22076

20300

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

6.637

22077

6976

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

6.638

22078

15782

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

6.638

22079

24997

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

6.638

22080

7415

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

6.641

22081

8973

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

6.641

22082

18615

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

6.642

22083

4231

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

6.644

22084

19961

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

6.645

22085

14511

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

6.646

22086

17130

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

6.647

22087

27426

\begin{align*} 2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \\ \end{align*}

6.649

22088

11964

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

6.653

22089

9945

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

Series expansion around \(x=0\).

6.656

22090

15354

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

6.657

22091

9934

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

Series expansion around \(x=0\).

6.658

22092

14508

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \\ y \left (0\right ) &= 6 \\ \end{align*}

6.660

22093

4409

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

6.661

22094

9658

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

6.664

22095

11530

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

6.665

22096

27482

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

6.666

22097

20798

\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*}

6.667

22098

4210

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

6.672

22099

1204

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

6.673

22100

14889

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

6.676