4.31 Problems 3001 to 3100

Table 4.61: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

3001

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

3002

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

3003

\[ {}y^{\prime } = 1-x^{5}+\sqrt {x} \]

3004

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

3005

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

3006

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

3007

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

3008

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

3009

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

3010

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

3011

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

3012

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

3013

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

3014

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

3015

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

3016

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

3017

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

3018

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

3019

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

3020

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

3021

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

3022

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

3023

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

3024

\[ {}y^{\prime } = \frac {3 x -y+1}{3 y-x +5} \]

3025

\[ {}3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0 \]

3026

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

3027

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

3028

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

3029

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

3030

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

3031

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

3032

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

3033

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

3034

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

3035

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

3036

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

3037

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

3038

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

3039

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

3040

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

3041

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

3042

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

3043

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

3044

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

3045

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

3046

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

3047

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

3048

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

3049

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

3050

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

3051

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

3052

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

3053

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

3054

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

3055

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

3056

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

3057

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

3058

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

3059

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

3060

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

3061

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

3062

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

3063

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

3064

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

3065

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

3066

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

3067

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

3068

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

3069

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

3070

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

3071

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

3072

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

3073

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

3074

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

3075

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

3076

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

3077

\[ {}x y y^{\prime } = \sqrt {y^{2}-9} \]

3078

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

3079

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

3080

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

3081

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

3082

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

3083

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

3084

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

3085

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

3086

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

3087

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

3088

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

3089

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

3090

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

3091

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

3092

\[ {}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \]

3093

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

3094

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

3095

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

3096

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

3097

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

3098

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

3099

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

3100

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