2.31 Problems 3001 to 3100

Table 2.31: Main lookup table

#

ODE

Mathematica result

Maple result

3001

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

3002

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

3003

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

3004

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

3005

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

3006

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

3007

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

3008

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

3009

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

3010

\[ {}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0 \]

3011

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

3012

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

3013

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

3014

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

3015

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

3016

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

3017

\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2} \]

3018

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

3019

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

3020

\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}-a y^{3} \]

3021

\[ {}x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3} = 0 \]

3022

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

3023

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

3024

\[ {}x^{2} y^{\prime } = \sec \relax (y)+3 x \tan \relax (y) \]

3025

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

3026

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

3027

\[ {}\left (-x^{2}+1\right ) y^{\prime } = 5-x y \]

3028

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

3029

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

3030

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

3031

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

3032

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

3033

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

3034

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

3035

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

3036

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

3037

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

3038

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

3039

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

3040

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

3041

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

3042

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

3043

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

3044

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

3045

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

3046

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

3047

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

3048

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

3049

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

3050

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

3051

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

3052

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

3053

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

3054

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

3055

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

3056

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

3057

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

3058

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

3059

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

3060

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

3061

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

3062

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

3063

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

3064

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

3065

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

3066

\[ {}\left (-2+x \right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y = 0 \]

3067

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

3068

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

3069

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

3070

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

3071

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

3072

\[ {}\left (x -a \right ) \left (x -b \right ) y^{\prime } = c y^{2} \]

3073

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

3074

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

3075

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

3076

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

3077

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

3078

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

3079

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

3080

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

3081

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

3082

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

3083

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

3084

\[ {}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (1+2 x \right ) y \]

3085

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

3086

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

3087

\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \]

3088

\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = c x y \ln \relax (y) \]

3089

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

3090

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

3091

\[ {}x^{3} y^{\prime } = a +b \,x^{2} y \]

3092

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

3093

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

3094

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

3095

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

3096

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

3097

\[ {}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0 \]

3098

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

3099

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

3100

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