3.9.14 Problems 1301 to 1400

Table 3.533: First order ode linear in derivative

#

ODE

Mathematica

Maple

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

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

3235

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

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

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

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

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

3278

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

3279

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

3280

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

3281

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

3282

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

3283

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

3284

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

3285

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

3286

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

3287

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

3288

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

3289

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

3290

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

3291

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

3292

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

3293

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

3294

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

3295

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

3296

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

3297

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

3298

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

3299

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

3300

\[ {}y^{\prime } = 6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right ) \]

3301

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

3302

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

3303

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

3304

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

3305

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

3306

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

3307

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

3308

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

3309

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

3310

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

3311

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

3312

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

3313

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

3314

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

3315

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

3316

\[ {}y^{\prime } = \left (1+4 x +9 y\right )^{2} \]

3317

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

3318

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

3319

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

3320

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

3321

\[ {}y^{\prime } = a \,x^{n -1}+b \,x^{2 n}+c y^{2} \]

3322

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

3323

\[ {}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2} \]

3324

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

3325

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

3326

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

3327

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

3328

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

3329

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

3330

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

3331

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

3332

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

3333

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

3334

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

3335

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

3336

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

3337

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

3338

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

3339

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

3340

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

3341

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

3342

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

3343

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

3344

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

3345

\[ {}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \]

3346

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

3347

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

3348

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