2.3.250 Problems 24901 to 25000

Table 2.1073: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24901

26091

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

16.577

24902

12023

\begin{align*} y^{\prime }&=\frac {\left (a y^{2}+b \,x^{2}\right )^{3} x}{a^{{5}/{2}} \left (a y^{2}+b \,x^{2}+a \right ) y} \\ \end{align*}

16.582

24903

6576

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

16.591

24904

740

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

16.594

24905

2987

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

16.599

24906

5037

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

16.599

24907

5244

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

16.602

24908

9014

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

16.635

24909

7862

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

16.653

24910

27082

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

16.656

24911

27260

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

16.661

24912

2901

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

16.675

24913

5506

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

16.682

24914

19236

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

16.709

24915

8720

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

16.715

24916

27479

\begin{align*} 2 x +3 y-1+\left (4 x +6 y-5\right ) y^{\prime }&=0 \\ \end{align*}

16.722

24917

5496

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

16.737

24918

26664

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

16.739

24919

22522

\begin{align*} r^{2} \sin \left (t \right )&=\left (2 r \cos \left (t \right )+10\right ) r^{\prime } \\ \end{align*}

16.740

24920

26314

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

16.740

24921

13713

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

16.754

24922

13754

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

16.760

24923

19923

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

16.763

24924

5688

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

16.776

24925

2533

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

16.779

24926

15943

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

16.783

24927

22947

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

16.799

24928

4317

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

16.812

24929

1217

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

16.818

24930

18050

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

16.829

24931

12484

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

16.833

24932

24400

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

16.834

24933

17114

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

16.835

24934

4139

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

16.851

24935

15528

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

16.870

24936

18613

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

16.880

24937

1701

\begin{align*} 7 x +4 y+\left (4 x +3 y\right ) y^{\prime }&=0 \\ \end{align*}

16.893

24938

7517

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

16.905

24939

7930

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

16.918

24940

2911

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

16.924

24941

22017

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

16.925

24942

20394

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

16.929

24943

20442

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

16.930

24944

24388

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

16.941

24945

116

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

16.947

24946

18552

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

16.949

24947

21805

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

16.950

24948

2939

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

16.952

24949

22573

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

16.964

24950

21555

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

16.966

24951

4401

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

16.973

24952

17047

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

16.987

24953

17976

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

16.999

24954

21398

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

17.003

24955

9481

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

17.011

24956

13422

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

17.052

24957

9197

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

17.070

24958

2358

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

17.093

24959

22465

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

17.098

24960

7866

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

17.145

24961

9147

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

17.155

24962

17229

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

17.158

24963

15052

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

17.174

24964

11468

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

17.177

24965

13366

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

17.178

24966

4316

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

17.197

24967

6194

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

17.206

24968

5029

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

17.209

24969

20292

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

17.232

24970

5304

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

17.237

24971

10430

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

17.243

24972

15645

\begin{align*} y^{\prime }&=x \sqrt {1-y^{2}} \\ y \left (0\right ) &= {\frac {9}{10}} \\ \end{align*}

17.255

24973

4304

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

17.273

24974

13052

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

17.279

24975

21764

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

17.283

24976

26262

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

17.296

24977

4348

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

17.300

24978

9205

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

17.320

24979

1161

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

17.329

24980

17471

\begin{align*} y^{\prime \prime }+9 \pi ^{2} y&=\left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

17.358

24981

24395

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

17.379

24982

24296

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

17.394

24983

26394

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

17.414

24984

22956

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

17.425

24985

19954

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

17.426

24986

2867

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

17.432

24987

9990

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

17.450

24988

12062

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

17.450

24989

11625

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

17.472

24990

15823

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

17.478

24991

27259

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

17.480

24992

2885

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

17.483

24993

5101

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

17.485

24994

22359

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

17.495

24995

1650

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

17.503

24996

8818

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

17.504

24997

9721

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

17.516

24998

16680

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=85 \cos \left (2 \ln \left (x \right )\right ) \\ \end{align*}

17.519

24999

20786

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

17.523

25000

14024

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

17.528