2.33 Problems 3201 to 3300

Table 2.33: Main lookup table

#

ODE

Mathematica result

Maple result

3201

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

3202

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

3203

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

3204

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

3205

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

3206

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

3207

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

3208

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

3209

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

3210

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

3211

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

3212

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

3213

\[ {}\left (1+x +2 y\right ) y^{\prime }+7+x -4 y = 0 \]

3214

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

3215

\[ {}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y \]

3216

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

3217

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

3218

\[ {}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0 \]

3219

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

3220

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

3221

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

3222

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

3223

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

3224

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

3225

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

3226

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

3227

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

3228

\[ {}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0 \]

3229

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

3230

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

3231

\[ {}\left (5+2 x -4 y\right ) y^{\prime } = 3+x -2 y \]

3232

\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \]

3233

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

3234

\[ {}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y \]

3235

\[ {}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y \]

3236

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

3237

\[ {}\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0 \]

3238

\[ {}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y \]

3239

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

3240

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

3241

\[ {}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0 \]

3242

\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \]

3243

\[ {}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0 \]

3244

\[ {}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y \]

3245

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

3246

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

3247

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

3248

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

3249

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

3250

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

3251

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

3252

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

3253

\[ {}x y y^{\prime } = a \,x^{3} \cos \relax (x )+y^{2} \]

3254

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

3255

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

3256

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

3257

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

3258

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

3259

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

3260

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

3261

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

3262

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

3263

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

3264

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

3265

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

3266

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

3267

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

3268

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

3269

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

3270

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

3271

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

3272

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

3273

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

3274

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

3275

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

3276

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

3277

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

3278

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

3279

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

3280

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

3281

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

3282

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

3283

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

3284

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

3285

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

3286

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

3287

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

3288

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

3289

\[ {}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2} \]

3290

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

3291

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

3292

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

3293

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

3294

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

3295

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

3296

\[ {}2 x \left (2 x^{2}+y\right ) y^{\prime }+\left (12 x^{2}+y\right ) y = 0 \]

3297

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

3298

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

3299

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

3300

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