3.1.14 Problems 1301 to 1400

Table 3.27: First order ode

#

ODE

Mathematica

Maple

3157

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

3158

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

3159

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

3160

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

3161

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

3162

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

3163

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

3164

\[ {}y^{\prime } = \left (1+x \right )^{2}+\left (4 y+1\right )^{2}+8 x y+1 \]

3165

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

3166

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

3167

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

3168

\[ {}3 y \left (x^{2}-1\right )+\left (x^{3}+8 y-3 x \right ) y^{\prime } = 0 \]

3169

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

3170

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

3171

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

3172

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

3173

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

3174

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

3175

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

3176

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

3177

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

3178

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

3179

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

3180

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

3181

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

3182

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

3183

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

3184

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

3185

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

3186

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

3187

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

3188

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

3189

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

3190

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

3191

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

3192

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

3193

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

3194

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

3195

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

3196

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

3197

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

3198

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

3199

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

3200

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

3201

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

3202

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

3203

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

3204

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

3205

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

3206

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

3207

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

3208

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

3209

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

3210

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

3211

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

3212

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

3213

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

3214

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

3215

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

3216

\[ {}y \left (6 y^{2}-x -1\right )+2 x y^{\prime } = 0 \]

3217

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

3218

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

3219

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

3220

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

3221

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

3222

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

3223

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

3224

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

3225

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

3226

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

3227

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

3228

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

3229

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

3230

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

3231

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

3232

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

3233

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

3234

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

3235

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

3236

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

3237

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

3238

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

3239

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

3240

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

3241

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

3264

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

3265

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

3266

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

3267

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

3268

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

3269

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

3270

\[ {}y^{\prime } = a +b \,{\mathrm e}^{k x}+c y \]

3271

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

3272

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

3273

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

3274

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

3275

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

3276

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

3277

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

3278

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