2.3.278 Problems 27701 to 27787

Table 2.1129: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

27701

20156

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

414.626

27702

5305

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

414.749

27703

13397

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

415.996

27704

12627

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

419.687

27705

26872

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

420.029

27706

26898

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

420.175

27707

25760

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

421.050

27708

20594

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

421.883

27709

23874

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

427.782

27710

25860

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

429.247

27711

13864

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

430.402

27712

13259

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

433.767

27713

10407

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

434.559

27714

14479

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

437.006

27715

27453

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

440.903

27716

13550

\begin{align*} y y^{\prime }-y&=-\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75} \\ \end{align*}

441.402

27717

20480

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

451.090

27718

24328

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

454.818

27719

26271

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

455.817

27720

26679

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

464.071

27721

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*}

465.243

27722

25655

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

466.247

27723

19658

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

467.554

27724

26154

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

469.667

27725

20769

\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*}

479.194

27726

26053

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

483.683

27727

23862

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

485.473

27728

25508

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

487.855

27729

9159

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

488.808

27730

20477

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

498.173

27731

13634

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

498.445

27732

21329

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

498.662

27733

26169

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

508.468

27734

19999

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

509.422

27735

20601

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

514.570

27736

25505

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

517.423

27737

20568

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

517.874

27738

15127

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

519.237

27739

20433

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

521.882

27740

26449

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

523.152

27741

6181

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

524.683

27742

21028

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

528.707

27743

13865

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

533.427

27744

10312

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

534.105

27745

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*}

550.113

27746

24897

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

550.113

27747

13260

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

552.357

27748

6358

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

560.101

27749

27300

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

569.703

27750

27423

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

579.215

27751

13827

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

586.213

27752

15036

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

606.068

27753

27490

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

617.938

27754

27255

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

620.671

27755

27611

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

636.684

27756

20430

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

682.009

27757

19998

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

684.507

27758

20013

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

716.943

27759

20732

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

731.178

27760

12505

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

734.075

27761

25086

\begin{align*} y^{\prime \prime }-y y^{\prime }&=6 \\ \end{align*}

790.796

27762

24815

\begin{align*} {y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\ \end{align*}

823.299

27763

12881

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

835.448

27764

15406

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

855.779

27765

21324

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

876.397

27766

21328

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

879.198

27767

26412

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

904.268

27768

20730

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

916.148

27769

24803

\begin{align*} {y^{\prime }}^{2}+4 x^{4} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

928.867

27770

26350

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

933.712

27771

13632

\begin{align*} x \left (\left (m -1\right ) \left (A x +B \right ) y+m \left (d \,x^{2}+e x +F \right )\right ) y^{\prime }&=\left (A \left (1-n \right ) x -B n \right ) y^{2}+\left (d \left (2-n \right ) x^{2}+e \left (1-n \right ) x -F n \right ) y \\ \end{align*}

968.244

27772

27365

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

970.081

27773

12241

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

977.704

27774

13869

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

1014.590

27775

13868

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

1027.932

27776

12666

\begin{align*} y^{\prime \prime }&=-\left (\frac {1-\operatorname {a1} -\operatorname {b1}}{x -\operatorname {c1}}+\frac {1-\operatorname {a2} -\operatorname {b2}}{x -\operatorname {c2}}+\frac {1-\operatorname {a3} -\operatorname {b3}}{x -\operatorname {c3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {a1} \operatorname {b1} \left (\operatorname {c1} -\operatorname {c3} \right ) \left (\operatorname {c1} -\operatorname {c2} \right )}{x -\operatorname {c1}}+\frac {\operatorname {a2} \operatorname {b2} \left (\operatorname {c2} -\operatorname {c1} \right ) \left (\operatorname {c2} -\operatorname {c3} \right )}{x -\operatorname {c2}}+\frac {\operatorname {a3} \operatorname {b3} \left (\operatorname {c3} -\operatorname {c2} \right ) \left (\operatorname {c3} -\operatorname {c1} \right )}{x -\operatorname {c3}}\right ) y}{\left (x -\operatorname {c1} \right ) \left (x -\operatorname {c2} \right ) \left (x -\operatorname {c3} \right )} \\ \end{align*}

1117.693

27777

12670

\begin{align*} y^{\prime \prime }&=-\left (\frac {\left (1-\operatorname {al1} -\operatorname {bl1} \right ) \operatorname {b1}}{\operatorname {b1} x -\operatorname {a1}}+\frac {\left (1-\operatorname {al2} -\operatorname {bl2} \right ) \operatorname {b2}}{\operatorname {b2} x -\operatorname {a2}}+\frac {\left (1-\operatorname {al3} -\operatorname {bl3} \right ) \operatorname {b3}}{\operatorname {b3} x -\operatorname {a3}}\right ) y^{\prime }-\frac {\left (\frac {\operatorname {al1} \operatorname {bl1} \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right ) \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right )}{\operatorname {b1} x -\operatorname {a1}}+\frac {\operatorname {al2} \operatorname {bl2} \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right ) \left (\operatorname {a1} \operatorname {b2} -\operatorname {a2} \operatorname {b1} \right )}{\operatorname {b2} x -\operatorname {a2}}+\frac {\operatorname {al3} \operatorname {bl3} \left (-\operatorname {a1} \operatorname {b3} +\operatorname {a3} \operatorname {b1} \right ) \left (\operatorname {a2} \operatorname {b3} -\operatorname {a3} \operatorname {b2} \right )}{\operatorname {b3} x -\operatorname {a3}}\right ) y}{\left (\operatorname {b1} x -\operatorname {a1} \right ) \left (\operatorname {b2} x -\operatorname {a2} \right ) \left (\operatorname {b3} x -\operatorname {a3} \right )} \\ \end{align*}

1248.425

27778

3650

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

1304.962

27779

12671

\begin{align*} y^{\prime \prime }&=-\frac {\left (x^{2} \left (\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right )+\left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )+\left (x^{2}-\operatorname {a3} \right ) \left (x^{2}-\operatorname {a1} \right )\right )-\left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )}-\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\operatorname {a1} \right ) \left (x^{2}-\operatorname {a2} \right ) \left (x^{2}-\operatorname {a3} \right )} \\ \end{align*}

1347.449

27780

27495

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

1371.358

27781

6288

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (b -x \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (b -x \right )^{2} \left (c -x \right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

1379.480

27782

11795

\begin{align*} 9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2}&=0 \\ \end{align*}

1398.160

27783

5675

\begin{align*} {y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \\ \end{align*}

1405.746

27784

5606

\begin{align*} 9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2}&=0 \\ \end{align*}

1444.556

27785

10404

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

1538.779

27786

25044

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

2296.239

27787

20777

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

3241.424