2.3.158 Problems 15701 to 15800

Table 2.847: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

15701

19361

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

3.576

15702

9885

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\ \end{align*}

3.577

15703

8180

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

3.578

15704

23941

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

3.578

15705

900

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

3.579

15706

4965

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

3.579

15707

12972

\begin{align*} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0}&=0 \\ \end{align*}

3.579

15708

15669

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

3.579

15709

21546

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

3.579

15710

24111

\begin{align*} x^{2} y^{\prime \prime }+2 x^{4} y^{\prime }-2 y&=0 \\ \end{align*}
Series expansion around \(x=0\).

3.579

15711

14141

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

3.580

15712

4715

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

3.582

15713

15584

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

3.582

15714

19694

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

3.582

15715

4812

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

3.584

15716

5831

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

3.584

15717

7557

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

3.584

15718

10374

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

3.584

15719

780

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

3.585

15720

9052

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

3.585

15721

17147

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

3.585

15722

18479

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

3.587

15723

22573

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

3.587

15724

12932

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

3.588

15725

3561

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

3.589

15726

12881

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

3.589

15727

22381

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

3.589

15728

23058

\begin{align*} \cot \left (\theta \right ) r^{\prime }&=r+b \\ \end{align*}

3.589

15729

681

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

3.591

15730

7399

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

3.591

15731

22535

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

3.591

15732

693

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

3.592

15733

14967

\begin{align*} x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z&=0 \\ z \left (1\right ) &= 0 \\ z^{\prime }\left (1\right ) &= 5 \\ \end{align*}

3.592

15734

5935

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

3.593

15735

22463

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

3.593

15736

2381

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

3.595

15737

23740

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

3.595

15738

9050

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

3.597

15739

8210

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

3.598

15740

12176

\begin{align*} y^{\prime }&=\frac {x +1+y^{4}-2 y^{2} x^{2}+x^{4}+y^{6}-3 x^{2} y^{4}+3 y^{2} x^{4}-x^{6}}{y} \\ \end{align*}

3.598

15741

1590

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

3.599

15742

12268

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

3.599

15743

25552

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{t} {\mathrm e}^{i t} \\ \end{align*}

3.600

15744

22375

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

3.601

15745

5683

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

3.602

15746

14200

\begin{align*} 2 x^{\prime \prime }-5 x^{\prime }-3 x&=0 \\ \end{align*}

3.602

15747

16701

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 8 \\ \end{align*}

3.602

15748

16289

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

3.604

15749

12013

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

3.605

15750

20822

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

3.605

15751

22102

\begin{align*} y^{\prime \prime }-y^{\prime }-30 y&=0 \\ \end{align*}

3.606

15752

14498

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

3.607

15753

5991

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

3.608

15754

7338

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

3.608

15755

16035

\begin{align*} y^{\prime \prime }-6 y^{\prime }-7 y&=0 \\ \end{align*}

3.608

15756

7936

\begin{align*} L i^{\prime }+R i&=E \sin \left (2 t \right ) \\ i \left (0\right ) &= 0 \\ \end{align*}

3.609

15757

19376

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

3.609

15758

21683

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

3.609

15759

4823

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

3.610

15760

11336

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

3.610

15761

14918

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

3.610

15762

23739

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

3.610

15763

16708

\begin{align*} y^{\prime \prime }+36 y&=0 \\ \end{align*}

3.611

15764

3450

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

3.612

15765

3451

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

3.612

15766

7391

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

3.612

15767

8211

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

3.612

15768

17188

\begin{align*} y+y^{\prime }&=4+3 \,{\mathrm e}^{t} \\ \end{align*}

3.612

15769

3976

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

3.613

15770

7530

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

3.613

15771

16201

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

3.613

15772

4861

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

3.614

15773

5285

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

3.614

15774

21439

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

3.614

15775

10046

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

3.615

15776

12436

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

3.615

15777

17042

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

3.615

15778

24223

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

3.615

15779

10449

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

3.616

15780

1327

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

3.617

15781

12271

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

3.617

15782

4355

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

3.618

15783

7320

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=8 x^{4} \\ \end{align*}

3.618

15784

16312

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

3.618

15785

3448

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

3.620

15786

7163

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

3.620

15787

23014

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

3.620

15788

7395

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

3.621

15789

11392

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

3.621

15790

16104

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=4+{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

3.621

15791

14721

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

3.622

15792

1694

\begin{align*} x^{2} {\mathrm e}^{y+x^{2}} \left (2 x^{2}+3\right )+4 x +\left (x^{3} {\mathrm e}^{y+x^{2}}-12 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

3.623

15793

7438

\begin{align*} \cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=2 x \cos \left (x \right )^{2} \\ y \left (\frac {\pi }{4}\right ) &= -\frac {15 \sqrt {2}\, \pi ^{2}}{32} \\ \end{align*}

3.623

15794

1186

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

3.625

15795

4199

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

3.625

15796

11692

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

3.625

15797

11892

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

3.626

15798

1545

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

3.627

15799

5887

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

3.627

15800

9228

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

3.628