2.3.258 Problems 25701 to 25800

Table 2.1065: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25701

10410

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

60.381

25702

4332

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

60.386

25703

6577

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

60.404

25704

11847

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

60.482

25705

7533

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

60.531

25706

17010

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

60.570

25707

11741

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

60.584

25708

6279

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

60.621

25709

22932

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

60.665

25710

11810

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

60.784

25711

25214

\begin{align*} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y&=0 \\ y \left (10\right ) &= y_{1} \\ y^{\prime }\left (10\right ) &= y_{1} \\ \end{align*}

60.806

25712

21837

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

60.846

25713

13997

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

60.890

25714

11450

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

60.897

25715

4415

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

60.994

25716

25185

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

61.001

25717

20319

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

61.123

25718

13740

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

61.140

25719

6084

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

61.254

25720

23218

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

61.348

25721

5181

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

61.364

25722

6453

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

61.368

25723

6197

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

61.596

25724

11992

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

61.694

25725

25007

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

61.724

25726

13828

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

61.907

25727

13444

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

61.945

25728

5585

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

62.148

25729

7743

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

62.239

25730

6171

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

62.325

25731

4331

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

62.401

25732

19121

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

62.537

25733

6278

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

62.594

25734

11551

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

62.622

25735

12450

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

62.626

25736

21327

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

62.753

25737

8725

\begin{align*} y^{\prime }&=-\frac {4 x +3 y+15}{2 x +y+7} \\ \end{align*}

62.780

25738

13382

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

62.783

25739

19048

\begin{align*} x_{1}^{\prime }&=2 x_{1}+x_{2}+1 \\ x_{2}^{\prime }&=x_{1}-2 x_{2}+x_{3} \\ x_{3}^{\prime }&=x_{2}-x_{3} \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= 0 \\ x_{2} \left (0\right ) &= 0 \\ x_{3} \left (0\right ) &= 0 \\ \end{align*}

62.857

25740

788

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

62.884

25741

13215

\begin{align*} y^{\prime }&=a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \\ \end{align*}

62.884

25742

16198

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

62.884

25743

21385

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

62.915

25744

6082

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

62.983

25745

22077

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

63.063

25746

21368

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

63.085

25747

17267

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

63.089

25748

5144

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

63.155

25749

6887

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

63.234

25750

20257

\begin{align*} \left (x -3 y+4\right ) y^{\prime }+7 y-5 x&=0 \\ \end{align*}

63.270

25751

11946

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

63.307

25752

25648

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

63.310

25753

13429

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

63.323

25754

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*}

63.415

25755

14834

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

63.505

25756

4084

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

63.516

25757

13497

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

63.523

25758

22466

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

63.690

25759

13978

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

63.772

25760

11360

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

63.787

25761

13610

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

63.804

25762

11935

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

63.836

25763

12126

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

63.865

25764

13633

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

64.003

25765

7125

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

64.031

25766

13476

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

64.043

25767

5259

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

64.284

25768

2881

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

64.471

25769

6198

\begin{align*} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

64.519

25770

7492

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

64.647

25771

2502

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

64.713

25772

2514

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

64.731

25773

8715

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

64.744

25774

13534

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

64.764

25775

25215

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

64.867

25776

13533

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

64.923

25777

25496

\begin{align*} y^{\prime }&=\frac {c t -a y}{A t +b y} \\ \end{align*}

65.322

25778

4820

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

65.623

25779

4851

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

65.672

25780

19114

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

65.714

25781

5005

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

65.872

25782

8708

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

65.946

25783

6560

\begin{align*} \left (\left (-y+a \right ) \left (-y+b \right )+\left (-y+a \right ) \left (c -y\right )+\left (-y+b \right ) \left (c -y\right )\right ) {y^{\prime }}^{2}+2 \left (-y+a \right ) \left (-y+b \right ) \left (c -y\right ) y^{\prime \prime }&=\operatorname {a3} \left (-y+a \right )^{2} \left (-y+b \right )^{2}+2 \operatorname {a2} \left (-y+a \right )^{2} \left (c -y\right )^{2}+\operatorname {a1} \left (-y+b \right )^{2} \left (c -y\right )^{2}+\operatorname {a0} \left (-y+a \right )^{2} \left (-y+b \right )^{2} \left (c -y\right )^{2} \\ \end{align*}

66.057

25784

12915

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

66.072

25785

11557

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

66.079

25786

13574

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

66.132

25787

11548

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

66.164

25788

13421

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

66.367

25789

13268

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

66.446

25790

4708

\begin{align*} y^{\prime }&=a +b y-\sqrt {A +B y} \\ \end{align*}

66.456

25791

14068

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

66.469

25792

22376

\begin{align*} U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\ \end{align*}

66.487

25793

1165

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

66.503

25794

13510

\begin{align*} y y^{\prime }-y&=\frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}} \\ \end{align*}

66.569

25795

5684

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

66.692

25796

19071

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

66.911

25797

18557

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

66.973

25798

21325

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

67.083

25799

6900

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

67.135

25800

5618

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

67.362