3.1.13 Problems 1201 to 1300

Table 3.25: First order ode

#

ODE

Mathematica

Maple

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

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

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

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

3101

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

3102

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

3103

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

3104

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

3105

\[ {}x y^{\prime } = x^{5}+x^{3} y^{2}+y \]

3106

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

3107

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

3108

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

3109

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

3110

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

3111

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

3112

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

3113

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

3114

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

3115

\[ {}2 x +3 y+1+\left (2 y-3 x +5\right ) y^{\prime } = 0 \]

3116

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

3117

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

3118

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

3119

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

3120

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

3121

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

3122

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

3123

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

3124

\[ {}6 x +4 y+3+\left (3 x +2 y+2\right ) y^{\prime } = 0 \]

3125

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

3126

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

3127

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

3128

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

3129

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

3130

\[ {}2 x y+\left (x^{2}+1\right ) y^{\prime } = 4 x^{3} \]

3131

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

3132

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

3133

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

3134

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

3135

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

3136

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

3137

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

3138

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

3139

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

3140

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

3141

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

3142

\[ {}r y^{\prime } = \frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \]

3143

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

3144

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

3145

\[ {}y^{2} y^{\prime } = 2+3 y^{6} \]

3146

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

3147

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

3148

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

3149

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

3150

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

3151

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

3152

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

3153

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

3154

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

3155

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

3156

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