6.31 Problems 3001 to 3100

Table 6.61: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

3001

\[ {} 2 y = \left (x^{2} y^{4}+x \right ) y^{\prime } \]

3002

\[ {} 1+x y \left (x y^{2}+1\right ) y^{\prime } = 0 \]

3003

\[ {} \left (-x^{2}+1\right ) y^{\prime }+x y = x \left (-x^{2}+1\right ) \sqrt {y} \]

3004

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

3005

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

3006

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

3007

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

3008

\[ {} x -2 y+1+\left (y-2\right ) y^{\prime } = 0 \]

3009

\[ {} 2 x y-2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 x^{2} y^{2}\right ) y^{\prime } = 0 \]

3010

\[ {} 2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime } = 0 \]

3011

\[ {} 6+2 y = x y y^{\prime } \]

3012

\[ {} x -3 y = \left (3 y-x +2\right ) y^{\prime } \]

3013

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

3014

\[ {} x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0 \]

3015

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

3016

\[ {} \tan \left (y\right ) = \left (3 x +4\right ) y^{\prime } \]

3017

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

3018

\[ {} 2 x y+y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime } = 0 \]

3019

\[ {} y+\left (3 x -2 y\right ) y^{\prime } = 0 \]

3020

\[ {} r^{\prime } = r \cot \left (\theta \right ) \]

3021

\[ {} \left (3 x +4 y\right ) y^{\prime }+y+2 x = 0 \]

3022

\[ {} 2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime } = 0 \]

3023

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

3024

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

3025

\[ {} x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0 \]

3026

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

3027

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

3028

\[ {} 3 x -6 = x y y^{\prime } \]

3029

\[ {} x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \]

3030

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

3031

\[ {} x y^{\prime }+y \left (1+y^{2}\right ) = 0 \]

3032

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

3033

\[ {} 3 \,{\mathrm e}^{x} \tan \left (y\right ) = \left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } \]

3034

\[ {} \sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x} \]

3035

\[ {} 2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 x y-y^{2}\right ) y^{\prime } = 0 \]

3036

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

3037

\[ {} y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime } = 0 \]

3038

\[ {} x +\left (2 x +3 y+2\right ) y^{\prime } = 0 \]

3039

\[ {} x y^{\prime }-5 y-x \sqrt {y} = 0 \]

3040

\[ {} x \sqrt {1-y}-\sqrt {-x^{2}+1}\, y^{\prime } = 0 \]

3041

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

3042

\[ {} x \,{\mathrm e}^{-y^{2}}+y y^{\prime } = 0 \]

3043

\[ {} \frac {2 y^{3}-2 x^{2} y^{3}-x +x y^{2} \ln \left (y\right )}{x y^{2}}+\frac {\left (2 y^{3} \ln \left (x \right )-x^{2} y^{3}+2 x +x y^{2}\right ) y^{\prime }}{y^{3}} = 0 \]

3044

\[ {} x y^{\prime }-2 y-2 x^{4} y^{3} = 0 \]

3045

\[ {} \left (-2 x^{2}-3 x y\right ) y^{\prime }+y^{2} = 0 \]

3046

\[ {} x y^{\prime } = x^{4}+4 y \]

3047

\[ {} y+x y^{\prime } = x^{3} y^{6} \]

3048

\[ {} x^{\prime } = x+x^{2} {\mathrm e}^{\theta } \]

3049

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

3050

\[ {} 3 x y+\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0 \]

3051

\[ {} y^{\prime }+2 y = 3 \,{\mathrm e}^{2 x} \]

3052

\[ {} 4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \]

3053

\[ {} x -2 y+3 = \left (x -2 y+1\right ) y^{\prime } \]

3054

\[ {} y^{2}+\left (x^{3}-2 x y\right ) y^{\prime } = 0 \]

3055

\[ {} 2 x y-2 y+1+x \left (x -1\right ) y^{\prime } = 0 \]

3056

\[ {} y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0 \]

3057

\[ {} 2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y \]

3058

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

3059

\[ {} y^{\prime \prime }-4 y = 0 \]

3060

\[ {} y^{\prime \prime }+7 y^{\prime }+12 y = 0 \]

3061

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

3062

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = 0 \]

3063

\[ {} 2 y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]

3064

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

3065

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

3066

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

3067

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

3068

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

3069

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

3070

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 0 \]

3071

\[ {} y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y = 0 \]

3072

\[ {} y^{\prime \prime \prime }-7 y^{\prime }+6 y = 0 \]

3073

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \]

3074

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y = 0 \]

3075

\[ {} y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y = 0 \]

3076

\[ {} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y = 0 \]

3077

\[ {} 2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y = 0 \]

3078

\[ {} 12 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime } = 0 \]

3079

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = 0 \]

3080

\[ {} 4 y^{\prime \prime \prime }+2 y^{\prime \prime }-4 y^{\prime }+y = 0 \]

3081

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y = 0 \]

3082

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y = 0 \]

3083

\[ {} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y = 0 \]

3084

\[ {} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y = 0 \]

3085

\[ {} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime } = 0 \]

3086

\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \]

3087

\[ {} y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime } = 0 \]

3088

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

3089

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

3090

\[ {} 2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y = 0 \]

3091

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

3092

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

3093

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

3094

\[ {} 4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0 \]

3095

\[ {} 4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime } = 0 \]

3096

\[ {} y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y = 0 \]

3097

\[ {} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y = 0 \]

3098

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

3099

\[ {} y^{\prime \prime \prime }-8 y = 0 \]

3100

\[ {} y^{\prime \prime }-2 y^{\prime }+3 y = 0 \]