2.3.258 Problems 25701 to 25800

Table 2.1089: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25701

22972

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

26.312

25702

17066

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

26.314

25703

8378

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

26.333

25704

22412

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

26.336

25705

17289

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

26.387

25706

5070

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

26.398

25707

23216

\begin{align*} y^{\prime }&=\frac {3 x -2 y+7}{2 x +3 y+9} \\ \end{align*}

26.398

25708

5114

\begin{align*} \left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \\ \end{align*}

26.431

25709

13541

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

26.465

25710

3556

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

26.484

25711

3580

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

26.490

25712

18847

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

26.517

25713

11367

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

26.593

25714

17347

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

26.632

25715

13299

\begin{align*} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }&=y^{2}+k \,{\mathrm e}^{\nu x} y-m^{2}+k m \,{\mathrm e}^{\nu x} \\ \end{align*}

26.634

25716

13836

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

26.635

25717

9828

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

26.695

25718

21028

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

26.705

25719

18575

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

26.735

25720

25713

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

26.760

25721

22957

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

26.763

25722

21066

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

26.770

25723

12410

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

26.808

25724

17260

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

26.812

25725

12491

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

26.813

25726

13807

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

26.813

25727

12409

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

26.818

25728

26615

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

26.832

25729

11514

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

26.854

25730

13269

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

26.872

25731

24829

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

26.888

25732

4286

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

26.907

25733

17086

\begin{align*} x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \\ \end{align*}

26.936

25734

23225

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

26.941

25735

17652

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

26.943

25736

25750

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

26.952

25737

11901

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

26.967

25738

27228

\begin{align*} x^{2} y^{\prime }-2 \cos \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {9 \pi }{4} \\ \end{align*}

26.970

25739

12278

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

26.980

25740

5120

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

26.991

25741

15351

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

27.001

25742

15151

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

27.014

25743

11995

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

27.024

25744

1686

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

27.067

25745

5161

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

27.068

25746

24355

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

27.068

25747

25748

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

27.074

25748

22607

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

27.095

25749

24866

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

27.113

25750

26410

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

27.114

25751

1203

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

27.126

25752

27483

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

27.164

25753

9015

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

27.178

25754

3961

\begin{align*} y^{\prime }-3 y&=-10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}

Using Laplace transform method.

27.191

25755

13295

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

27.215

25756

21808

\begin{align*} 3 x^{2}+2 y x +4 y^{2}+\left (20 x^{2}+6 y x +y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

27.231

25757

22971

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

27.235

25758

1147

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

27.246

25759

12125

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

27.248

25760

21827

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

27.248

25761

20973

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

27.250

25762

3649

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

27.258

25763

14270

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

27.270

25764

27523

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

27.272

25765

12596

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

27.286

25766

3302

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

27.290

25767

11341

\begin{align*} y^{\prime }-\operatorname {a3} y^{3}-\operatorname {a2} y^{2}-\operatorname {a1} y-\operatorname {a0}&=0 \\ \end{align*}

27.300

25768

13256

\begin{align*} x^{2} y^{\prime }&=c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \\ \end{align*}

27.312

25769

2886

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

27.343

25770

6021

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

27.344

25771

12047

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

27.385

25772

12929

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

27.408

25773

24381

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

27.445

25774

8781

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

27.447

25775

13641

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

27.479

25776

18483

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

27.494

25777

19938

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

27.498

25778

12612

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

27.559

25779

18553

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

27.565

25780

18620

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

27.568

25781

14715

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

27.569

25782

13428

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

27.589

25783

19725

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

27.605

25784

17277

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

27.619

25785

17987

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

27.628

25786

22435

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

27.663

25787

11754

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

27.667

25788

12118

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

27.670

25789

12239

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

27.689

25790

9059

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

27.710

25791

6994

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

27.723

25792

12217

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

27.724

25793

22425

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

27.763

25794

13396

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

27.784

25795

19719

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

27.791

25796

2920

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

27.813

25797

4944

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

27.814

25798

17274

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

27.817

25799

1663

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

27.821

25800

25036

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

27.822