2.2.179 Problems 17801 to 17900

Table 2.371: 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]]

5.099

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]]

4.848

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]]

8.089

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]]

3.781

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]]

7.375

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]]

1.309

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]]

2.494

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]]

3.083

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]]

27.329

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]]

13.500

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]]

24.099

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]]

47.426

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]]

81.432

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]]

189.772

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]]

112.476

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]]

1.856

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]]

1.288

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]]

3.560

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]]

3.230

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]]

53.321

17821

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

system_of_ODEs

0.424

17822

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

system_of_ODEs

0.516

17823

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

system_of_ODEs

0.390

17824

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

system_of_ODEs

0.047

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

0.650

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

0.553

17827

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

system_of_ODEs

0.645

17828

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

system_of_ODEs

0.490

17829

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

system_of_ODEs

0.665

17830

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

system_of_ODEs

0.813

17831

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

system_of_ODEs

0.779

17832

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

system_of_ODEs

0.930

17833

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

[[_2nd_order, _missing_x]]

34.493

17834

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

[[_2nd_order, _missing_x]]

8.875

17835

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

[[_2nd_order, _linear, _nonhomogeneous]]

27.222

17836

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

[[_2nd_order, _with_linear_symmetries]]

2.579

17837

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

[[_Riccati, _special]]

69.965

17838

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

[_separable]

28.096

17839

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

[_quadrature]

5.892

17840

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

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

8.251

17841

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

57.466

17842

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

[_quadrature]

10.233

17843

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

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

52.755

17844

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

[‘y=_G(x,y’)‘]

3.485

17845

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

[_quadrature]

1.557

17846

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

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

6.823

17847

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

[‘y=_G(x,y’)‘]

2.112

17848

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

[_linear]

4.287

17849

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

[[_linear, ‘class A‘]]

3.419

17850

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

[_separable]

5.316

17851

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

[_quadrature]

0.405

17852

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

[[_linear, ‘class A‘]]

2.647

17853

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

[[_linear, ‘class A‘]]

2.048

17854

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

[[_linear, ‘class A‘]]

2.954

17855

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

[_quadrature]

0.435

17856

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

[_separable]

5.410

17857

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

[_Riccati]

31.370

17858

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

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

4.251

17859

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

[[_linear, ‘class A‘]]

4.047

17860

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

[[_linear, ‘class A‘]]

3.367

17861

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

[_separable]

5.872

17862

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

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

12.792

17863

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

[_quadrature]

0.432

17864

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

[[_linear, ‘class A‘]]

2.934

17865

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

[[_linear, ‘class A‘]]

3.973

17866

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

[_separable]

7.249

17867

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

[_quadrature]

1.099

17868

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

[_quadrature]

0.548

17869

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

[_quadrature]

1.248

17870

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

[_quadrature]

5.559

17871

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

[_Riccati]

32.131

17872

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

[[_Riccati, _special]]

793.290

17873

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

[[_linear, ‘class A‘]]

3.022

17874

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

[[_linear, ‘class A‘]]

24.901

17875

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

[_linear]

11.751

17876

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

[_separable]

7.217

17877

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

[_separable]

24.298

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]

7.452

17879

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

[_separable]

8.939

17880

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

[_separable]

8.587

17881

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

[_separable]

26.542

17882

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

[_quadrature]

1.626

17883

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

[_separable]

31.381

17884

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

[_separable]

9.074

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]

12.028

17886

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

[_separable]

10.696

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]

8.204

17888

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

[_separable]

24.855

17889

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

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

4.410

17890

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

[[_linear, ‘class A‘]]

4.471

17891

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

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

49.110

17892

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

[_linear]

23.553

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]

31.085

17894

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

[_separable]

27.360

17895

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

[_quadrature]

1.297

17896

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

[_quadrature]

0.871

17897

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

[_quadrature]

0.841

17898

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

[_quadrature]

2.046

17899

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

[_quadrature]

0.895

17900

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

[_quadrature]

0.680