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]]

3.549

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]]

2.230

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]]

3.875

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]]

2.331

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]]

2.419

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]]

0.450

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]]

0.529

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]]

0.523

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]]

0.606

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]]

0.533

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]]

0.536

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]]

3.440

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]]

1.608

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]]

3.296

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]]

13.428

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]]

0.714

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]]

0.637

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]]

0.766

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]]

0.741

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]]

0.910

17821

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

system_of_ODEs

0.441

17822

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

system_of_ODEs

0.511

17823

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

system_of_ODEs

0.356

17824

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

system_of_ODEs

0.040

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

0.621

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

0.574

17827

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

system_of_ODEs

0.548

17828

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

system_of_ODEs

0.419

17829

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

system_of_ODEs

0.560

17830

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

system_of_ODEs

0.701

17831

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

system_of_ODEs

0.722

17832

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

system_of_ODEs

0.823

17833

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

[[_2nd_order, _missing_x]]

0.429

17834

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

[[_2nd_order, _missing_x]]

0.446

17835

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.829

17836

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

[[_2nd_order, _with_linear_symmetries]]

0.504

17837

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

[[_Riccati, _special]]

12.220

17838

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

[_separable]

17.878

17839

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

[_quadrature]

5.635

17840

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

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

7.735

17841

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

23.424

17842

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

[_quadrature]

7.357

17843

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

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

24.931

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]

1.430

17846

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

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

5.688

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

[_linear]

2.872

17849

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

[[_linear, ‘class A‘]]

2.720

17850

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

[_separable]

9.140

17851

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

[_quadrature]

0.426

17852

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

[[_linear, ‘class A‘]]

2.208

17853

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

[[_linear, ‘class A‘]]

1.819

17854

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

[[_linear, ‘class A‘]]

2.363

17855

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

[_quadrature]

0.602

17856

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

[_separable]

4.329

17857

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

[_Riccati]

9.165

17858

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

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

3.245

17859

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

[[_linear, ‘class A‘]]

3.277

17860

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

[[_linear, ‘class A‘]]

2.681

17861

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

[_separable]

4.398

17862

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

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

18.415

17863

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

[_quadrature]

0.418

17864

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

[[_linear, ‘class A‘]]

2.388

17865

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

[[_linear, ‘class A‘]]

3.234

17866

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

[_separable]

5.790

17867

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

[_quadrature]

1.010

17868

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

[_quadrature]

0.714

17869

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

[_quadrature]

1.384

17870

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

[_quadrature]

4.761

17871

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

[_Riccati]

9.558

17872

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

[[_Riccati, _special]]

280.695

17873

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

[[_linear, ‘class A‘]]

2.390

17874

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

[[_linear, ‘class A‘]]

10.158

17875

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

[_linear]

9.273

17876

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

[_separable]

5.685

17877

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

[_separable]

10.597

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]

7.650

17879

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

[_separable]

6.719

17880

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

[_separable]

7.031

17881

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

[_separable]

12.096

17882

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

[_quadrature]

1.360

17883

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

[_separable]

7.334

17884

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

[_separable]

5.635

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]

9.227

17886

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

[_separable]

9.001

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]

6.980

17888

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

[_separable]

9.414

17889

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

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

3.424

17890

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

[[_linear, ‘class A‘]]

3.668

17891

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

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

22.116

17892

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

[_linear]

9.249

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]

13.954

17894

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

[_separable]

4.576

17895

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

[_quadrature]

1.408

17896

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

[_quadrature]

0.765

17897

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

[_quadrature]

0.550

17898

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

[_quadrature]

1.171

17899

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

[_quadrature]

0.796

17900

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

[_quadrature]

0.478