2.3.260 Problems 25901 to 26000

Table 2.1063: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25901

13897

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

119.592

25902

13814

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

119.593

25903

14475

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

119.766

25904

13616

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

119.967

25905

20745

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

120.121

25906

6087

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

120.460

25907

13597

\begin{align*} y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}}&=\frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}} \\ \end{align*}

120.541

25908

24182

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

120.724

25909

13467

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

120.985

25910

23122

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

121.122

25911

23903

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

121.124

25912

2915

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

121.316

25913

11703

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

121.380

25914

2909

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

121.618

25915

5308

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

121.657

25916

13520

\begin{align*} y y^{\prime }-y&=-\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

121.730

25917

5248

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

122.341

25918

14438

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

122.451

25919

14537

\begin{align*} y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \\ y \left (1\right ) &= 2 \\ \end{align*}

122.968

25920

23224

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

123.014

25921

17902

\begin{align*} x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\ y \left (\infty \right ) &= \frac {16 \pi }{3} \\ \end{align*}

123.111

25922

12576

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

123.387

25923

20151

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

123.480

25924

18352

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

123.835

25925

13517

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

124.021

25926

5673

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

124.345

25927

23875

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

124.363

25928

12525

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

124.468

25929

11296

\begin{align*} y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \\ \end{align*}

124.729

25930

13819

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

125.034

25931

7871

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

125.049

25932

19118

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

125.638

25933

13584

\begin{align*} y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}} \\ \end{align*}

125.790

25934

13588

\begin{align*} y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}} \\ \end{align*}

125.867

25935

3018

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

126.048

25936

12577

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

126.481

25937

13536

\begin{align*} y y^{\prime }-y&=\frac {63 x}{4}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

126.725

25938

23191

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

126.908

25939

6112

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

127.283

25940

13408

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

127.286

25941

13848

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

127.324

25942

18349

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

127.523

25943

21958

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

127.533

25944

6211

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

127.708

25945

23292

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

127.709

25946

5470

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

127.869

25947

12661

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

127.919

25948

5858

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

128.109

25949

16325

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

128.162

25950

5568

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

128.163

25951

13628

\begin{align*} \left (A x y+A k y+B \,x^{2}+B k x \right ) y^{\prime }&=c y^{2}+d x y+k \left (d -B \right ) y \\ \end{align*}

128.268

25952

19137

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

128.281

25953

14553

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

128.539

25954

14546

\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}

129.274

25955

14446

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

129.276

25956

13568

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

129.808

25957

13514

\begin{align*} y y^{\prime }-y&=-\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}} \\ \end{align*}

129.970

25958

12566

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

130.063

25959

13986

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

130.097

25960

14065

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

130.281

25961

21461

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

131.070

25962

20296

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

131.527

25963

12637

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

131.747

25964

6265

\begin{align*} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

132.211

25965

22476

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

132.289

25966

22770

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

132.403

25967

6264

\begin{align*} -\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

132.448

25968

7725

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

132.666

25969

6470

\begin{align*} 2 y y^{\prime \prime }&=8 y^{3}+{y^{\prime }}^{2} \\ \end{align*}

132.700

25970

20476

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

133.249

25971

10077

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

133.504

25972

20477

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

133.563

25973

23960

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

133.829

25974

13542

\begin{align*} y y^{\prime }-y&=20 x +\frac {A}{\sqrt {x}} \\ \end{align*}

133.845

25975

6209

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

134.286

25976

12604

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

134.572

25977

5569

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

134.625

25978

13999

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

134.877

25979

14010

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

136.406

25980

11584

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

136.679

25981

12950

\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}&=0 \\ \end{align*}

137.177

25982

11817

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

137.434

25983

21466

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

137.664

25984

13604

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

138.395

25985

11998

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

139.089

25986

6113

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

139.115

25987

11619

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

140.014

25988

24241

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

140.356

25989

6210

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

140.369

25990

11772

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

141.655

25991

13879

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

141.715

25992

22447

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

141.760

25993

22604

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

142.140

25994

18732

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

142.413

25995

19783

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

142.660

25996

21982

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

142.749

25997

10004

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

142.940

25998

13508

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

143.212

25999

13585

\begin{align*} y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}}&=-\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}} \\ \end{align*}

143.334

26000

18341

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

143.861