2.3.148 Problems 14701 to 14800

Table 2.839: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14701

18091

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

1.681

14702

23763

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

1.681

14703

7266

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

1.682

14704

14741

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

1.683

14705

209

\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}

1.684

14706

16950

\begin{align*} x^{\prime }&=2 x-5 y+4 \\ y^{\prime }&=3 x-7 y+5 \\ \end{align*}

1.685

14707

3541

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

1.686

14708

8741

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

1.686

14709

14926

\begin{align*} x^{\prime \prime }+6 x^{\prime }+10 x&=0 \\ x \left (0\right ) &= 3 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

1.686

14710

17098

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

1.686

14711

24944

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

1.686

14712

3268

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

1.687

14713

8718

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

1.688

14714

11712

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

1.688

14715

18806

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

1.688

14716

3960

\begin{align*} y^{\prime }-3 y&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right . \\ y \left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

1.689

14717

22683

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

1.689

14718

21949

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime } x&={\mathrm e}^{x}+1 \\ \end{align*}

1.690

14719

167

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

1.691

14720

3006

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

1.691

14721

18960

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=g \left (t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.691

14722

22074

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

1.691

14723

25202

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

1.691

14724

25418

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

1.691

14725

3244

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

1.693

14726

13020

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

1.693

14727

16010

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

1.693

14728

2487

\begin{align*} y+y^{\prime }&=\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

1.694

14729

9053

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

1.694

14730

25847

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

1.694

14731

12654

\begin{align*} y^{\prime \prime }&=\frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )} \\ \end{align*}

1.695

14732

20666

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

1.695

14733

24929

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

1.695

14734

16405

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

1.696

14735

15

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

1.697

14736

1110

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

1.697

14737

22622

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

1.697

14738

15335

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

1.698

14739

9735

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

1.699

14740

14753

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

1.699

14741

14744

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

1.700

14742

1505

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

1.701

14743

7261

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

1.701

14744

26191

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

1.702

14745

10371

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

1.703

14746

14239

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

1.703

14747

1618

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

1.704

14748

5952

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

1.704

14749

14263

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

1.704

14750

14752

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +\left (2 x^{2}+\frac {5}{9}\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.704

14751

23964

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

1.704

14752

16815

\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.705

14753

25200

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

1.705

14754

11863

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

1.706

14755

18376

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

1.706

14756

8324

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

1.707

14757

8888

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

1.707

14758

10233

\begin{align*} x^{\prime }&=x+2 y+2 t +1 \\ y^{\prime }&=5 x+y+3 t -1 \\ \end{align*}

1.707

14759

11391

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

1.707

14760

11736

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

1.707

14761

16797

\begin{align*} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

1.707

14762

21489

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

1.707

14763

24519

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

1.708

14764

16967

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

1.709

14765

25191

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

1.709

14766

609

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

1.710

14767

25225

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

1.710

14768

6287

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

1.711

14769

13288

\begin{align*} y^{\prime }&=y^{2}+a \,{\mathrm e}^{8 \lambda x}+b \,{\mathrm e}^{6 \lambda x}+c \,{\mathrm e}^{4 \lambda x}-\lambda ^{2} \\ \end{align*}

1.711

14770

8872

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

1.712

14771

18045

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

1.712

14772

20701

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

1.712

14773

14751

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

1.713

14774

10442

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

1.714

14775

11711

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

1.714

14776

16732

\begin{align*} 9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\ \end{align*}

1.715

14777

698

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

1.716

14778

25460

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

1.716

14779

221

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

1.717

14780

1301

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

1.717

14781

8276

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

1.717

14782

8463

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

1.717

14783

15845

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

1.717

14784

16556

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\ \end{align*}

1.717

14785

3388

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

1.718

14786

14668

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

1.718

14787

25281

\begin{align*} y^{\prime \prime }+a^{2} y&=f \left (t \right ) \\ \end{align*}
Using Laplace transform method.

1.719

14788

801

\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}

1.720

14789

14061

\begin{align*} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 y^{\prime } x -1&=0 \\ \end{align*}

1.720

14790

17462

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=4 \\ y \left (0\right ) &= {\frac {5}{4}} \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

1.720

14791

20390

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

1.720

14792

6530

\begin{align*} \operatorname {f3} \left (x \right ) y^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f0} \left (x \right ) y y^{\prime \prime }&=0 \\ \end{align*}

1.722

14793

7131

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

1.722

14794

17712

\begin{align*} 7 y^{\prime \prime } x +10 y^{\prime }+\left (-x^{2}+1\right ) y&=0 \\ \end{align*}
Series expansion around \(x=0\).

1.722

14795

6067

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

1.723

14796

9441

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

1.723

14797

902

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\ \end{align*}

1.724

14798

1120

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

1.724

14799

6494

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

1.724

14800

12187

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

1.725