2.2.179 Problems 17801 to 17900

Table 2.375: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

17801

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

[[_2nd_order, _missing_x]]

2.950

17802

\begin{align*} x^{\prime \prime }+16 x&=0 \\ x \left (0\right ) &= -2 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.623

17803

\begin{align*} x^{\prime \prime }+256 x&=0 \\ x \left (0\right ) &= 2 \\ x^{\prime }\left (0\right ) &= 4 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.313

17804

\begin{align*} x^{\prime \prime }+9 x&=0 \\ x \left (0\right ) &= {\frac {1}{3}} \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.714

17805

\begin{align*} 10 x^{\prime \prime }+\frac {x}{10}&=0 \\ x \left (0\right ) &= -5 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.219

17806

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

[[_2nd_order, _missing_x]]

0.401

17807

\begin{align*} \frac {x^{\prime \prime }}{32}+2 x^{\prime }+x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.490

17808

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

[[_2nd_order, _missing_x]]

0.479

17809

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

[[_2nd_order, _missing_x]]

0.599

17810

\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.550

17811

\begin{align*} x^{\prime \prime }+4 x^{\prime }+20 x&=0 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= 2 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.528

17812

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.676

17813

\begin{align*} x^{\prime \prime }+x&=\left \{\begin {array}{cc} \cos \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

29.934

17814

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

[[_2nd_order, _linear, _nonhomogeneous]]

4.176

17815

\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=\left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 1-t & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right . \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

18.386

17816

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.750

17817

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.661

17818

\begin{align*} x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.731

17819

\begin{align*} x^{\prime \prime }+x&=\cos \left (\frac {7 t}{10}\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.740

17820

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \cos \left (2 t \right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.961

17821

\begin{align*} x^{\prime }&=6 \\ y^{\prime }&=\cos \left (t \right ) \\ \end{align*}

system_of_ODEs

0.444

17822

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

system_of_ODEs

0.523

17823

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

system_of_ODEs

0.391

17824

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

system_of_ODEs

0.025

17825

\begin{align*} x_{1}^{\prime }&=-3 x_{1} \\ x_{2}^{\prime }&=1 \\ \end{align*}
With initial conditions
\begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 1 \\ \end{align*}

system_of_ODEs

0.634

17826

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

system_of_ODEs

0.569

17827

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

system_of_ODEs

0.607

17828

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

system_of_ODEs

0.474

17829

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

system_of_ODEs

0.636

17830

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

system_of_ODEs

0.759

17831

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

system_of_ODEs

0.988

17832

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

system_of_ODEs

0.932

17833

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

[[_2nd_order, _missing_x]]

0.396

17834

\begin{align*} x^{\prime \prime }+6 x^{\prime }+9 x&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.376

17835

\begin{align*} x^{\prime \prime }+16 x&=t \sin \left (t \right ) \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.881

17836

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

[[_2nd_order, _with_linear_symmetries]]

0.464

17837

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

[[_Riccati, _special]]

15.358

17838

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

[_separable]

25.645

17839

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

[_quadrature]

7.901

17840

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

[[_homogeneous, ‘class C‘], _dAlembert]

10.270

17841

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

35.985

17842

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

[_quadrature]

9.242

17843

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

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

37.872

17844

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

[‘y=_G(x,y’)‘]

3.239

17845

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

[_quadrature]

1.478

17846

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

[[_homogeneous, ‘class C‘], _dAlembert]

7.802

17847

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

[‘y=_G(x,y’)‘]

1.558

17848

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

[_linear]

3.538

17849

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

[[_linear, ‘class A‘]]

3.303

17850

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

[_separable]

11.005

17851

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

[_quadrature]

0.430

17852

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

[[_linear, ‘class A‘]]

3.680

17853

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

[[_linear, ‘class A‘]]

2.160

17854

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

[[_linear, ‘class A‘]]

2.890

17855

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

[_quadrature]

0.598

17856

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

[_separable]

5.233

17857

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

[_Riccati]

11.076

17858

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

[[_homogeneous, ‘class C‘], _dAlembert]

3.842

17859

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

[[_linear, ‘class A‘]]

3.964

17860

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

[[_linear, ‘class A‘]]

3.253

17861

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

[_separable]

6.521

17862

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

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

26.099

17863

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

[_quadrature]

1.411

17864

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

[[_linear, ‘class A‘]]

2.922

17865

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

[[_linear, ‘class A‘]]

4.012

17866

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

[_separable]

7.001

17867

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

[_quadrature]

1.073

17868

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

[_quadrature]

0.683

17869

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

[_quadrature]

1.415

17870

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

[_quadrature]

5.948

17871

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

[_Riccati]

11.999

17872

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

[[_Riccati, _special]]

27.168

17873

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

[[_linear, ‘class A‘]]

3.829

17874

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

[[_linear, ‘class A‘]]

14.226

17875

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

[_linear]

13.375

17876

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

[_separable]

6.393

17877

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

[_separable]

13.147

17878

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

[_separable]

7.601

17879

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

[_separable]

7.286

17880

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

[_separable]

7.623

17881

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

[_separable]

13.997

17882

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

[_quadrature]

1.502

17883

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

[_separable]

9.277

17884

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

[_separable]

7.964

17885

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

[_separable]

11.504

17886

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

[_separable]

11.424

17887

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

[_separable]

7.838

17888

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

[_separable]

12.219

17889

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

[[_homogeneous, ‘class C‘], _dAlembert]

3.887

17890

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

[[_linear, ‘class A‘]]

4.691

17891

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

[[_homogeneous, ‘class C‘], _dAlembert]

32.373

17892

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

[_linear]

13.967

17893

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

[_separable]

24.511

17894

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

[_separable]

6.684

17895

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

[_quadrature]

1.547

17896

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

[_quadrature]

0.817

17897

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

[_quadrature]

0.665

17898

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

[_quadrature]

1.602

17899

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

[_quadrature]

0.857

17900

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

[_quadrature]

0.603