2.2.101 Problems 10001 to 10100

Table 2.219: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

10001

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

[_quadrature]

0.672

10002

\begin{align*} y^{\prime }&=\frac {-y x -1}{4 x^{3} y-2 x^{2}} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

121.228

10003

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.349

10004

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

[_quadrature]

200.454

10005

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

[‘y=_G(x,y’)‘]

2.369

10006

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

[_Bernoulli]

2.089

10007

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

[[_1st_order, _with_linear_symmetries], _Chini]

105.909

10008

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

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

55.136

10009

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

[_separable]

1.921

10010

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

[_quadrature]

0.151

10011

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

[_quadrature]

0.351

10012

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

[_quadrature]

0.122

10013

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

[_quadrature]

0.340

10014

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

[_quadrature]

0.329

10015

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

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

0.643

10016

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

[[_homogeneous, ‘class A‘], _rational, _Riccati]

3.928

10017

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

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

9.570

10018

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

[_quadrature]

0.786

10019

\begin{align*} p^{\prime }&=a p-b p^{2} \\ p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\ \end{align*}

[_quadrature]

5.122

10020

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

[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli]

3.474

10021

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

[_Clairaut]

5.876

10022

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

[_rational, _Riccati]

2.187

10023

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

[_rational, _Riccati]

51.581

10024

\begin{align*} u^{\prime }+u^{2}&=\frac {1}{x^{{4}/{5}}} \\ \end{align*}

[_rational, _Riccati]

0.434

10025

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

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

8.649

10026

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

[[_2nd_order, _missing_x]]

0.308

10027

\begin{align*} 5 y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.494

10028

\begin{align*} y^{\prime \prime }+y^{\prime }+4 y&=1 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.458

10029

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.448

10030

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

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

1.971

10031

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

[_dAlembert]

90.918

10032

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

[_quadrature]

1.298

10033

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

[[_2nd_order, _missing_y]]

0.957

10034

\begin{align*} \left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime }&=0 \\ y \left (3\right ) &= 2 \pi \\ y^{\prime }\left (3\right ) &= {\frac {2}{3}} \\ \end{align*}

[[_2nd_order, _missing_y]]

0.822

10035

\begin{align*} t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.410

10036

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

[[_2nd_order, _missing_y]]

0.710

10037

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

[[_2nd_order, _missing_y]]

0.596

10038

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

[[_2nd_order, _with_linear_symmetries]]

13.026

10039

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

[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.173

10040

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

[[_2nd_order, _quadrature]]

0.500

10041

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

[[_2nd_order, _quadrature]]

0.906

10042

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

[[_2nd_order, _quadrature]]

0.692

10043

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

[[_2nd_order, _quadrature]]

0.675

10044

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

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

24.362

10045

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

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

1.616

10046

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

[[_2nd_order, _quadrature]]

0.751

10047

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

[[_2nd_order, _quadrature]]

0.054

10048

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.007

10049

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

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.315

10050

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

[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

0.352

10051

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

[[_2nd_order, _quadrature]]

0.055

10052

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

[NONE]

0.385

10053

\begin{align*} 3 y y^{\prime \prime }+y&=5 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

20.455

10054

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

2.025

10055

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

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

75.468

10056

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

[[_2nd_order, _quadrature]]

0.079

10057

\begin{align*} x^{\prime }&=9 x+4 y \\ y^{\prime }&=-6 x-y \\ z^{\prime }&=6 x+4 y+3 z \\ \end{align*}

system_of_ODEs

0.571

10058

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

system_of_ODEs

0.323

10059

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

system_of_ODEs

0.312

10060

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

system_of_ODEs

0.328

10061

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

system_of_ODEs

0.429

10062

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

system_of_ODEs

0.522

10063

\begin{align*} x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \\ \end{align*}

[_quadrature]

97.989

10064

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

[[_homogeneous, ‘class A‘], _dAlembert]

1.006

10065

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

[[_homogeneous, ‘class A‘], _dAlembert]

0.974

10066

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

[_separable]

122.758

10067

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

[[_Riccati, _special]]

6.247

10068

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

[_quadrature]

5.803

10069

\begin{align*} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.477

10070

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

[_quadrature]

3.712

10071

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

[_Riccati]

24.213

10072

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

[_Bernoulli]

2.056

10073

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

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

48.467

10074

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

[[_2nd_order, _missing_x]]

0.379

10075

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

[[_2nd_order, _missing_x]]

0.349

10076

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

[[_2nd_order, _missing_x]]

0.453

10077

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

[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

61.333

10078

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

[_Riccati]

8.433

10079

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

[[_2nd_order, _with_linear_symmetries]]

0.732

10080

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

[[_2nd_order, _with_linear_symmetries]]

0.621

10081

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

[[_2nd_order, _with_linear_symmetries]]

0.629

10082

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

[[_2nd_order, _with_linear_symmetries]]

0.852

10083

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.910

10084

\begin{align*} y^{\prime \prime }-x y^{\prime }-y x -x^{4}-6&=0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.855

10085

\begin{align*} y^{\prime \prime }-x y^{\prime }-y x -x^{5}+24&=0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.879

10086

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

[[_2nd_order, _with_linear_symmetries]]

0.585

10087

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

[[_2nd_order, _with_linear_symmetries]]

0.795

10088

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.852

10089

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

[[_2nd_order, _with_linear_symmetries]]

3.404

10090

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

[[_2nd_order, _with_linear_symmetries]]

2.260

10091

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

[[_2nd_order, _linear, _nonhomogeneous]]

2.350

10092

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

[[_2nd_order, _with_linear_symmetries]]

0.260

10093

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.933

10094

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

[[_2nd_order, _with_linear_symmetries]]

0.259

10095

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

[[_2nd_order, _with_linear_symmetries]]

0.261

10096

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

[[_2nd_order, _with_linear_symmetries]]

0.276

10097

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

[[_2nd_order, _with_linear_symmetries]]

0.270

10098

\begin{align*} y^{\prime \prime }-y^{\prime }-y x -x^{3}+1&=0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

0.890

10099

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.267

10100

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.271