2.2.91 Problems 9001 to 9100

Table 2.183: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

9001

\[ {}c y^{\prime } = y \]

[_quadrature]

0.900

9002

\[ {}c y^{\prime } = b y \]

[_quadrature]

0.967

9003

\[ {}c y^{\prime } = a x +b y^{2} \]

[[_Riccati, _special]]

1.210

9004

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r} \]

[[_Riccati, _special]]

1.227

9005

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r x} \]

[_rational, _Riccati]

4.059

9006

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{r \,x^{2}} \]

[_rational, _Riccati]

6.378

9007

\[ {}c y^{\prime } = \frac {a x +b y^{2}}{y} \]

[_rational, _Bernoulli]

1.753

9008

\[ {}a \sin \left (x \right ) y x y^{\prime } = 0 \]

[_quadrature]

0.597

9009

\[ {}f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi = 0 \]

[_quadrature]

0.583

9010

\[ {}y^{\prime } = \sin \left (x \right )+y \]

[[_linear, ‘class A‘]]

1.423

9011

\[ {}y^{\prime } = \sin \left (x \right )+y^{2} \]

[_Riccati]

2.941

9012

\[ {}y^{\prime } = \cos \left (x \right )+\frac {y}{x} \]

[_linear]

1.533

9013

\[ {}y^{\prime } = \cos \left (x \right )+\frac {y^{2}}{x} \]

[_Riccati]

5.191

9014

\[ {}y^{\prime } = x +y+b y^{2} \]

[_Riccati]

1.223

9015

\[ {}x y^{\prime } = 0 \]

[_quadrature]

0.431

9016

\[ {}5 y^{\prime } = 0 \]

[_quadrature]

0.432

9017

\[ {}{\mathrm e} y^{\prime } = 0 \]

[_quadrature]

0.465

9018

\[ {}\pi y^{\prime } = 0 \]

[_quadrature]

0.458

9019

\[ {}\sin \left (x \right ) y^{\prime } = 0 \]

[_quadrature]

0.533

9020

\[ {}f \left (x \right ) y^{\prime } = 0 \]

[_quadrature]

0.467

9021

\[ {}x y^{\prime } = 1 \]

[_quadrature]

0.512

9022

\[ {}x y^{\prime } = \sin \left (x \right ) \]

[_quadrature]

0.586

9023

\[ {}\left (-1+x \right ) y^{\prime } = 0 \]

[_quadrature]

0.432

9024

\[ {}y y^{\prime } = 0 \]

[_quadrature]

0.541

9025

\[ {}x y y^{\prime } = 0 \]

[_quadrature]

0.550

9026

\[ {}x y \sin \left (x \right ) y^{\prime } = 0 \]

[_quadrature]

0.572

9027

\[ {}\pi y \sin \left (x \right ) y^{\prime } = 0 \]

[_quadrature]

0.585

9028

\[ {}x \sin \left (x \right ) y^{\prime } = 0 \]

[_quadrature]

0.483

9029

\[ {}x \sin \left (x \right ) {y^{\prime }}^{2} = 0 \]

[_quadrature]

0.150

9030

\[ {}y {y^{\prime }}^{2} = 0 \]

[_quadrature]

0.148

9031

\[ {}{y^{\prime }}^{n} = 0 \]

[_quadrature]

0.572

9032

\[ {}x {y^{\prime }}^{n} = 0 \]

[_quadrature]

0.577

9033

\[ {}{y^{\prime }}^{2} = x \]

[_quadrature]

0.286

9034

\[ {}{y^{\prime }}^{2} = x +y \]

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

0.626

9035

\[ {}{y^{\prime }}^{2} = \frac {y}{x} \]

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

2.449

9036

\[ {}{y^{\prime }}^{2} = \frac {y^{2}}{x} \]

[_separable]

1.424

9037

\[ {}{y^{\prime }}^{2} = \frac {y^{3}}{x} \]

[[_homogeneous, ‘class G‘]]

0.901

9038

\[ {}{y^{\prime }}^{3} = \frac {y^{2}}{x} \]

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

1.080

9039

\[ {}{y^{\prime }}^{2} = \frac {1}{x y} \]

[[_homogeneous, ‘class G‘]]

0.751

9040

\[ {}{y^{\prime }}^{2} = \frac {1}{x y^{3}} \]

[[_homogeneous, ‘class G‘]]

0.783

9041

\[ {}{y^{\prime }}^{2} = \frac {1}{x^{2} y^{3}} \]

[_separable]

0.793

9042

\[ {}{y^{\prime }}^{4} = \frac {1}{x y^{3}} \]

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

1.196

9043

\[ {}{y^{\prime }}^{2} = \frac {1}{x^{3} y^{4}} \]

[_separable]

1.013

9044

\[ {}y^{\prime } = \sqrt {1+6 x +y} \]

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

2.625

9045

\[ {}y^{\prime } = \left (1+6 x +y\right )^{{1}/{3}} \]

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

2.017

9046

\[ {}y^{\prime } = \left (1+6 x +y\right )^{{1}/{4}} \]

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

1.659

9047

\[ {}y^{\prime } = \left (a +b x +y\right )^{4} \]

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

159.482

9048

\[ {}y^{\prime } = \left (\pi +x +7 y\right )^{{7}/{2}} \]

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

17.236

9049

\[ {}y^{\prime } = \left (a +b x +c y\right )^{6} \]

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

5.819

9050

\[ {}y^{\prime } = {\mathrm e}^{x +y} \]

[_separable]

2.599

9051

\[ {}y^{\prime } = 10+{\mathrm e}^{x +y} \]

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

2.456

9052

\[ {}y^{\prime } = 10 \,{\mathrm e}^{x +y}+x^{2} \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

1.515

9053

\[ {}y^{\prime } = x \,{\mathrm e}^{x +y}+\sin \left (x \right ) \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

2.099

9054

\[ {}y^{\prime } = 5 \,{\mathrm e}^{x^{2}+20 y}+\sin \left (x \right ) \]

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

2.161

9055

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ] \]

system_of_ODEs

0.172

9056

\[ {}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x=y+t \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ] \]

system_of_ODEs

0.910

9057

\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ] \]

system_of_ODEs

0.361

9058

\[ {}t y^{\prime }+y = t \]
i.c.

[_linear]

0.304

9059

\[ {}y^{\prime }-t y = 0 \]
i.c.

[_separable]

0.409

9060

\[ {}t y^{\prime }+y = 0 \]
i.c.

[_separable]

0.401

9061

\[ {}t y^{\prime }+y = 0 \]
i.c.

[_separable]

0.300

9062

\[ {}t y^{\prime }+y = 0 \]
i.c.

[_separable]

0.452

9063

\[ {}t y^{\prime }+y = 0 \]

[_separable]

0.301

9064

\[ {}t y^{\prime }+y = 0 \]
i.c.

[_separable]

0.579

9065

\[ {}t y^{\prime }+y = \sin \left (t \right ) \]
i.c.

[_linear]

0.673

9066

\[ {}t y^{\prime }+y = t \]
i.c.

[_linear]

0.568

9067

\[ {}t y^{\prime }+y = t \]
i.c.

[_linear]

0.638

9068

\[ {}y^{\prime }+t^{2} y = 0 \]
i.c.

[_separable]

0.401

9069

\[ {}\left (a t +1\right ) y^{\prime }+y = t \]
i.c.

[_linear]

0.409

9070

\[ {}y^{\prime }+\left (a t +t b \right ) y = 0 \]
i.c.

[_separable]

0.313

9071

\[ {}y^{\prime }+\left (a t +t b \right ) y = 0 \]
i.c.

[_separable]

0.349

9072

\[ {}y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

1.880

9073

\[ {}{y^{\prime \prime }}^{2} = 0 \]

[[_2nd_order, _quadrature]]

0.441

9074

\[ {}{y^{\prime \prime }}^{n} = 0 \]

[[_2nd_order, _quadrature]]

0.270

9075

\[ {}a y^{\prime \prime } = 0 \]

[[_2nd_order, _quadrature]]

1.988

9076

\[ {}a {y^{\prime \prime }}^{2} = 0 \]

[[_2nd_order, _quadrature]]

0.459

9077

\[ {}a {y^{\prime \prime }}^{n} = 0 \]

[[_2nd_order, _quadrature]]

0.200

9078

\[ {}y^{\prime \prime } = 1 \]

[[_2nd_order, _quadrature]]

2.107

9079

\[ {}{y^{\prime \prime }}^{2} = 1 \]

[[_2nd_order, _quadrature]]

1.560

9080

\[ {}y^{\prime \prime } = x \]

[[_2nd_order, _quadrature]]

1.740

9081

\[ {}{y^{\prime \prime }}^{2} = x \]

[[_2nd_order, _quadrature]]

0.422

9082

\[ {}{y^{\prime \prime }}^{3} = 0 \]

[[_2nd_order, _quadrature]]

0.510

9083

\[ {}y^{\prime \prime }+y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

1.752

9084

\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = 0 \]

[[_2nd_order, _missing_x]]

2.329

9085

\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 0 \]

[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

0.373

9086

\[ {}y^{\prime \prime }+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

1.846

9087

\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = 1 \]

[[_2nd_order, _missing_x]]

2.025

9088

\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \]

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

1.525

9089

\[ {}y^{\prime \prime }+y^{\prime } = x \]

[[_2nd_order, _missing_y]]

1.888

9090

\[ {}{y^{\prime \prime }}^{2}+y^{\prime } = x \]

[[_2nd_order, _missing_y]]

0.760

9091

\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = x \]

[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]

0.602

9092

\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

2.074

9093

\[ {}{y^{\prime \prime }}^{2}+y^{\prime }+y = 0 \]

[[_2nd_order, _missing_x]]

0.052

9094

\[ {}y^{\prime \prime }+{y^{\prime }}^{2}+y = 0 \]

[[_2nd_order, _missing_x]]

1.984

9095

\[ {}y^{\prime \prime }+y^{\prime }+y = 1 \]

[[_2nd_order, _missing_x]]

15.274

9096

\[ {}y^{\prime \prime }+y^{\prime }+y = x \]

[[_2nd_order, _with_linear_symmetries]]

17.944

9097

\[ {}y^{\prime \prime }+y^{\prime }+y = x +1 \]

[[_2nd_order, _with_linear_symmetries]]

23.416

9098

\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2}+x +1 \]

[[_2nd_order, _with_linear_symmetries]]

34.199

9099

\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1 \]

[[_2nd_order, _linear, _nonhomogeneous]]

25.026

9100

\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \]

[[_2nd_order, _linear, _nonhomogeneous]]

45.608