2.2.31 Problems 3001 to 3100

Table 2.79: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

3001

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

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

3.690

3002

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

[_rational, _Bernoulli]

2.059

3003

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

[_separable]

2.150

3004

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

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

45.951

3005

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

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

10.779

3006

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

[_linear]

1.608

3007

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

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

7.241

3008

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

[_exact, _rational]

2.455

3009

\begin{align*} 2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime }&=0 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

2.517

3010

\begin{align*} 2 y+6&=x y y^{\prime } \\ \end{align*}

[_separable]

4.075

3011

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

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

6.342

3012

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

[_exact]

32.535

3013

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

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

1.078

3014

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

[_separable]

3.019

3015

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

[_separable]

3.208

3016

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

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

2.204

3017

\begin{align*} 2 y x +y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

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

4.240

3018

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

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

18.785

3019

\begin{align*} r^{\prime }&=r \cot \left (\theta \right ) \\ \end{align*}

[_separable]

2.770

3020

\begin{align*} \left (3 x +4 y\right ) y^{\prime }+2 x +y&=0 \\ \end{align*}

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

7.800

3021

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

[_rational, _Bernoulli]

2.275

3022

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

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

5.563

3023

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

[_separable]

2.836

3024

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

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

16.566

3025

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

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

10.171

3026

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

[_linear]

2.052

3027

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

[_separable]

2.345

3028

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

[_exact]

2.786

3029

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

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

10.303

3030

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

[_separable]

6.205

3031

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

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

21.096

3032

\begin{align*} 3 \,{\mathrm e}^{x} \tan \left (y\right )&=\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } \\ \end{align*}

[_separable]

4.076

3033

\begin{align*} \sec \left (y\right )^{2} y^{\prime }&=\tan \left (y\right )+2 x \,{\mathrm e}^{x} \\ \end{align*}

[‘y=_G(x,y’)‘]

3.624

3034

\begin{align*} 2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 y x -y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_exact]

16.056

3035

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

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

30.615

3036

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

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

63.698

3037

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

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

9.457

3038

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

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

8.000

3039

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

[_separable]

4.143

3040

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

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

4.780

3041

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

[_separable]

2.634

3042

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

[_exact]

4.404

3043

\begin{align*} x y^{\prime }-2 y-2 x^{4} y^{3}&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

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

5.147

3044

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

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

1.762

3045

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

[_linear]

2.638

3046

\begin{align*} x y^{\prime }+y&=x^{3} y^{6} \\ y \left (1\right ) &= 1 \\ \end{align*}

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

5.540

3047

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

2.078

3048

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

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

10.503

3049

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

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

19.636

3050

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

[[_linear, ‘class A‘]]

1.983

3051

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

[_separable]

3.709

3052

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

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

8.043

3053

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

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

61.862

3054

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

[_linear]

2.212

3055

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

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

28.303

3056

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

[_separable]

7.747

3057

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

[_quadrature]

0.888

3058

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

[[_2nd_order, _missing_x]]

2.749

3059

\begin{align*} y^{\prime \prime }+7 y^{\prime }+12 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.270

3060

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

[[_2nd_order, _missing_x]]

0.280

3061

\begin{align*} y^{\prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.276

3062

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

[[_2nd_order, _missing_x]]

0.277

3063

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

[[_2nd_order, _missing_x]]

0.306

3064

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

[[_2nd_order, _missing_x]]

0.296

3065

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

[[_2nd_order, _missing_x]]

0.303

3066

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

[[_2nd_order, _missing_x]]

0.314

3067

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

[[_3rd_order, _missing_x]]

0.049

3068

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.049

3069

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

[[_3rd_order, _missing_x]]

0.056

3070

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.054

3071

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }+6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.045

3072

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.047

3073

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.048

3074

\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.048

3075

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.055

3076

\begin{align*} 2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.060

3077

\begin{align*} 12 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.056

3078

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

[[_3rd_order, _missing_x]]

0.047

3079

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

[[_3rd_order, _missing_x]]

0.056

3080

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.052

3081

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.056

3082

\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.064

3083

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.069

3084

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.061

3085

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

[[_high_order, _missing_x]]

0.055

3086

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.067

3087

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

[[_2nd_order, _missing_x]]

0.337

3088

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

[[_2nd_order, _quadrature]]

0.550

3089

\begin{align*} 2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.049

3090

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

[[_3rd_order, _missing_x]]

0.046

3091

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

[[_high_order, _quadrature]]

0.043

3092

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

[[_3rd_order, _missing_x]]

0.051

3093

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

[[_3rd_order, _missing_x]]

0.049

3094

\begin{align*} 4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime }&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.057

3095

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.053

3096

\begin{align*} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.053

3097

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

[[_high_order, _missing_x]]

0.050

3098

\begin{align*} y^{\prime \prime \prime }-8 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.055

3099

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

[[_2nd_order, _missing_x]]

0.396

3100

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.058