2.3.251 Problems 25001 to 25100

Table 2.1075: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25001

11534

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

17.536

25002

17225

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

17.539

25003

5847

\begin{align*} \left (\operatorname {a0} -\operatorname {a2} \csc \left (x \right )^{2}+4 \operatorname {a1} \sin \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

17.549

25004

14013

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

17.555

25005

27024

\begin{align*} y^{\prime \prime \prime }-8 y&=\left \{\begin {array}{cc} 0 & 0\le t <6 \\ 2 & 6\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

17.555

25006

26915

\begin{align*} y^{\prime }&=\frac {2 y+x +7}{-2 x +y-9} \\ \end{align*}

17.556

25007

7955

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

17.598

25008

2859

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

17.615

25009

19107

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

17.619

25010

24957

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

17.621

25011

15523

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

17.623

25012

11953

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

17.626

25013

17230

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

17.638

25014

4693

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

17.643

25015

14869

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

17.647

25016

5942

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

17.651

25017

15183

\begin{align*} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y&=0 \\ \end{align*}

17.666

25018

18064

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

17.668

25019

13623

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

17.669

25020

26316

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

17.671

25021

27432

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

17.676

25022

19906

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

17.678

25023

22399

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

17.679

25024

13024

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

17.694

25025

4083

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

17.695

25026

19411

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

17.699

25027

10434

\begin{align*} x y^{\prime \prime }-y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \\ \end{align*}

17.707

25028

8711

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

17.726

25029

19916

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

17.734

25030

24226

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

17.737

25031

7485

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

17.747

25032

7712

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

17.748

25033

21396

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

17.758

25034

24297

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

17.764

25035

18603

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

17.769

25036

25746

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

17.770

25037

24161

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

17.774

25038

6483

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

17.787

25039

1752

\begin{align*} \left (3 x -1\right ) y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\left (6 x -8\right ) y&=0 \\ \end{align*}

17.813

25040

12928

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

17.822

25041

12094

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

17.834

25042

4803

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

17.864

25043

12481

\begin{align*} x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2 n}+\operatorname {b1} \,x^{n}+\operatorname {c1} \right ) y&=0 \\ \end{align*}

17.865

25044

1658

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

17.868

25045

4266

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

17.873

25046

17838

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

17.878

25047

13624

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

17.896

25048

19287

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

17.919

25049

22500

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

17.954

25050

22601

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

17.974

25051

6424

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

17.980

25052

18558

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

17.981

25053

4417

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

18.000

25054

7475

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

18.011

25055

1194

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

18.016

25056

13458

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

18.026

25057

11589

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

18.055

25058

21597

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

18.066

25059

18878

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

18.069

25060

7724

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

18.071

25061

4886

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

18.107

25062

18068

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

18.118

25063

13838

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

18.121

25064

17309

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

18.125

25065

26259

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

18.140

25066

17287

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

18.143

25067

13370

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

18.177

25068

15136

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

18.192

25069

5925

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

18.211

25070

13214

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

18.212

25071

12163

\begin{align*} y^{\prime }&=\frac {\left (a^{3}+y^{4} a^{3}+2 a^{2} y^{2} b \,x^{2}+b^{2} x^{4} a +y^{6} a^{3}+3 y^{4} a^{2} b \,x^{2}+3 y^{2} a \,b^{2} x^{4}+b^{3} x^{6}\right ) x}{a^{{7}/{2}} y} \\ \end{align*}

18.221

25072

19068

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

18.232

25073

3655

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

18.252

25074

22571

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

18.254

25075

21389

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

18.270

25076

20262

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

18.276

25077

16858

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

Series expansion around \(x=2\).

18.286

25078

17265

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

18.299

25079

14163

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

18.336

25080

14549

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

18.336

25081

6556

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

18.342

25082

12264

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

18.353

25083

26606

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (2 x \right )+\sin \left (2 x \right ) \\ y \left (-\infty \right ) &= y_{0} \\ \end{align*}

18.355

25084

5016

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

18.372

25085

11499

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

18.373

25086

5332

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

18.379

25087

8692

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

18.381

25088

19282

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

18.402

25089

22545

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

18.408

25090

21455

\begin{align*} y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\ \end{align*}

18.414

25091

17862

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

18.415

25092

14896

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

18.428

25093

25899

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

18.482

25094

13511

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

18.500

25095

21129

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

18.523

25096

9057

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

18.533

25097

8722

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

18.535

25098

13345

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

18.550

25099

22405

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

18.563

25100

8780

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

18.566