2.3.107 Problems 10601 to 10700

Table 2.745: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

10601

25774

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (8\right ) &= -4 \\ \end{align*}

1.406

10602

8203

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

1.407

10603

11303

\begin{align*} y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \\ \end{align*}

1.407

10604

15370

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

1.407

10605

6547

\begin{align*} 2 \left (1-y\right ) y y^{\prime \prime }&=-\left (1-y\right )^{3} \left (\operatorname {F0} \left (x \right )^{2}-\operatorname {G0} \left (x \right )^{2} y^{2}\right )-4 \left (1-y\right ) y^{2} \left (f \left (x \right )^{2}-g \left (x \right )^{2}+f^{\prime }\left (x \right )+g^{\prime }\left (x \right )\right )-4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2} \\ \end{align*}

1.408

10606

14846

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

1.408

10607

15928

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

1.408

10608

5815

\begin{align*} b \,{\mathrm e}^{x k} y+a y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

1.410

10609

12700

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

1.411

10610

25293

\begin{align*} y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \\ \end{align*}
Using Laplace transform method.

1.411

10611

1110

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

1.412

10612

16259

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

1.412

10613

21323

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

1.412

10614

21662

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

1.412

10615

22803

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

1.412

10616

5209

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

1.413

10617

5211

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

1.413

10618

15854

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

1.413

10619

22070

\begin{align*} y^{\prime }+6 y x&=0 \\ y \left (\pi \right ) &= 5 \\ \end{align*}

1.413

10620

1916

\begin{align*} \left (\beta \,x^{2}+x \alpha +1\right ) y^{\prime \prime }+\left (\delta x +\gamma \right ) y^{\prime }+\epsilon y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.414

10621

2072

\begin{align*} 4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (9-x \right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.414

10622

3440

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

1.414

10623

5696

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

1.414

10624

5955

\begin{align*} x^{2} y^{\prime \prime }&=6 y \\ \end{align*}

1.414

10625

17133

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

1.414

10626

22318

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

1.414

10627

2104

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

1.415

10628

10109

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

1.415

10629

16154

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

1.415

10630

20585

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

1.415

10631

21003

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

1.415

10632

22539

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

1.415

10633

24797

\begin{align*} {y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\ \end{align*}

1.415

10634

2838

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

1.416

10635

9729

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

1.416

10636

9951

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

1.416

10637

17990

\begin{align*} 4 {y^{\prime }}^{2}-9 x&=0 \\ \end{align*}

1.416

10638

1736

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= -1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.417

10639

79

\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ \end{align*}

1.418

10640

726

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

1.420

10641

7620

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

1.420

10642

9415

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

1.420

10643

19156

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

1.420

10644

20775

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

1.420

10645

9036

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

1.421

10646

9818

\begin{align*} 16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6}&=0 \\ \end{align*}

1.421

10647

13319

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

1.421

10648

24966

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

1.421

10649

25046

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

1.421

10650

22589

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

1.423

10651

2323

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

1.424

10652

14242

\begin{align*} x^{\prime }&=2 t^{3} x-6 \\ \end{align*}

1.424

10653

18055

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

1.424

10654

14557

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 7 \\ \end{align*}

1.425

10655

24913

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

1.425

10656

24066

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

1.427

10657

24766

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

1.427

10658

25296

\begin{align*} y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.427

10659

69

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

1.428

10660

165

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

1.428

10661

8864

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

1.428

10662

12961

\begin{align*} 2 y y^{\prime \prime }-6 {y^{\prime }}^{2}+y^{2} \left (1+a y^{3}\right )&=0 \\ \end{align*}

1.428

10663

15122

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

1.428

10664

16810

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

1.428

10665

20394

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

1.429

10666

22552

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

1.429

10667

5821

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

1.430

10668

2087

\begin{align*} x^{2} \left (2 x +1\right ) y^{\prime \prime }-x \left (9+8 x \right ) y^{\prime }-12 y x&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.431

10669

4582

\begin{align*} x_{1}^{\prime }&=x_{1}-x_{2}-x_{3}+4 \,{\mathrm e}^{t} \\ x_{2}^{\prime }&=x_{1}+x_{2} \\ x_{3}^{\prime }&=3 x_{1}+x_{3} \\ \end{align*}

1.431

10670

14701

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

1.431

10671

21318

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

1.431

10672

22226

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

1.431

10673

24999

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

1.431

10674

10551

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

1.433

10675

22048

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

1.433

10676

5602

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

1.434

10677

21258

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

1.434

10678

25808

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

1.434

10679

6051

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

1.435

10680

25

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

1.436

10681

5435

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

1.436

10682

8652

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=10 \sin \left (t \right )+10 \delta \left (t -1\right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*}
Using Laplace transform method.

1.436

10683

15837

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

1.436

10684

16687

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

1.436

10685

16922

\begin{align*} y^{\prime \prime } x +4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}}&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.436

10686

8449

\begin{align*} T^{\prime }&=k \left (T-T_{m} \right ) \\ T \left (0\right ) &= T_{0} \\ \end{align*}

1.437

10687

25432

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

1.437

10688

3918

\begin{align*} x_{1}^{\prime }&=2 x_{1}-2 x_{2}+x_{3}+t \\ x_{2}^{\prime }&=x_{1}-4 x_{2}+x_{3} \\ x_{3}^{\prime }&=2 x_{1}+2 x_{2}-3 x_{3}+1 \\ \end{align*}

1.438

10689

14510

\begin{align*} \left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \\ y \left (0\right ) &= 4 \\ \end{align*}

1.438

10690

22040

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

1.438

10691

22050

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

1.439

10692

4743

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

1.440

10693

20390

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

1.440

10694

20985

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

1.440

10695

6303

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

1.441

10696

20873

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

1.441

10697

5463

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

1.442

10698

7261

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

1.442

10699

7022

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

1.443

10700

15234

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+5 y&=25 t \left (\operatorname {Heaviside}\left (t \right )-\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right )\right ) \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

1.443