2.3.258 Problems 25701 to 25800

Table 2.1059: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25701

6197

\begin{align*} \operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

90.431

25702

13534

\begin{align*} y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\ \end{align*}

90.661

25703

23188

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

90.727

25704

22466

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

90.759

25705

12857

\begin{align*} y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \\ \end{align*}

90.819

25706

13470

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

90.852

25707

8834

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

91.459

25708

12635

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

91.480

25709

13572

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

91.546

25710

22345

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

91.779

25711

18722

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

91.937

25712

13817

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

91.958

25713

6146

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

92.082

25714

25886

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

92.121

25715

13469

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

92.165

25716

13407

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

92.171

25717

17052

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (4\right ) &= -5 \\ \end{align*}

92.370

25718

11816

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

92.487

25719

4975

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

92.525

25720

20327

\begin{align*} y^{\prime }+\frac {a x +b y+c}{b x +f y+e}&=0 \\ \end{align*}

92.583

25721

6860

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

92.763

25722

19901

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

92.806

25723

23289

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

93.184

25724

6074

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

93.210

25725

21324

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

93.271

25726

8323

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

93.301

25727

6257

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

93.378

25728

25213

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

93.398

25729

6139

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

93.423

25730

5249

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

93.431

25731

13887

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

93.520

25732

12590

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

93.665

25733

6326

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

93.708

25734

23133

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

93.716

25735

13343

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

93.759

25736

25800

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

93.786

25737

6147

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

93.892

25738

8833

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

93.900

25739

9685

\begin{align*} x^{\prime }&=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }&=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }&=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \\ \end{align*}

93.912

25740

5110

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

94.049

25741

5006

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

94.647

25742

13913

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

94.691

25743

13349

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

95.205

25744

13334

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

95.244

25745

5674

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

95.340

25746

23127

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

95.754

25747

13619

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

95.783

25748

21264

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

95.916

25749

22605

\begin{align*} y^{\prime }&=\sqrt {\frac {5 x -6 y}{5 x +6 y}} \\ \end{align*}

95.956

25750

5005

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

96.101

25751

13401

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

96.409

25752

17051

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (3\right ) &= -6 \\ \end{align*}

96.506

25753

20433

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

97.241

25754

13896

\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*}

97.529

25755

22012

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

97.530

25756

5202

\begin{align*} 8 y y^{\prime } x^{3}+3 x^{4}-6 y^{2} x^{2}-y^{4}&=0 \\ \end{align*}

97.667

25757

19905

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

97.718

25758

19999

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

98.914

25759

25007

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

99.031

25760

13923

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

99.291

25761

14476

\begin{align*} 3 x^{2}+9 y x +5 y^{2}-\left (6 x^{2}+4 y x \right ) y^{\prime }&=0 \\ y \left (2\right ) &= -6 \\ \end{align*}

99.696

25762

21464

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

99.760

25763

6261

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

99.941

25764

12237

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

100.014

25765

13480

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

100.441

25766

6072

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

100.523

25767

13598

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

100.614

25768

19395

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

100.687

25769

19817

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

100.919

25770

13611

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

100.979

25771

17275

\begin{align*} 2 t^{2}-7 t y+5 y^{2}+t y y^{\prime }&=0 \\ \end{align*}

100.984

25772

12236

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

101.083

25773

11770

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

101.750

25774

17906

\begin{align*} {\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\ \end{align*}

101.966

25775

13815

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

102.308

25776

11844

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

102.336

25777

25715

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

102.431

25778

20035

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

102.626

25779

13581

\begin{align*} y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}} \\ \end{align*}

103.098

25780

6224

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

103.122

25781

12574

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

103.791

25782

9820

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

104.095

25783

13601

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

104.141

25784

20966

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

104.165

25785

5460

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

104.318

25786

13579

\begin{align*} y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}}&=-\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}} \\ \end{align*}

104.345

25787

18342

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

104.433

25788

5122

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

104.655

25789

15932

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

104.936

25790

13337

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

104.952

25791

12630

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

105.165

25792

12513

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

105.208

25793

4882

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

105.223

25794

7966

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

105.704

25795

11609

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

105.816

25796

6318

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

105.847

25797

12072

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

105.975

25798

12856

\begin{align*} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y&=0 \\ \end{align*}

106.090

25799

12655

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

106.168

25800

15361

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

106.227