4.14.1 Problems 1 to 100

Table 4.845: First order ode non-linear in derivative

#

ODE

Mathematica

Maple

Sympy

70

\[ {} {y^{\prime }}^{2} = 4 y \]

98

\[ {} \frac {1-4 x y^{2}}{x^{\prime }} = y^{3} \]

99

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

100

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

169

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

3285

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

3286

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

3287

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

3288

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

3289

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

3290

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

3291

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

3292

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

3293

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

3294

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

3295

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

3296

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

3297

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

3298

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

3299

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

3300

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

3301

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

3302

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

3303

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

3304

\[ {} 8 x +1 = y {y^{\prime }}^{2} \]

3305

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

3306

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

3307

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

3308

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

3309

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

3310

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

3311

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

3312

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

3313

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

3314

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

3315

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

3316

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

3317

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

3318

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

3319

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

3320

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

3321

\[ {} 3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1 \]

3322

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

3323

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

3324

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

3325

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

3326

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

3327

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

3328

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

3329

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

3330

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

3331

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

3332

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

3333

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

3334

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

3414

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

3415

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

4087

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

4088

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

4089

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

4383

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

4384

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

4385

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

4386

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

4387

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

4388

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

4389

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

4390

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

4391

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

4392

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

4393

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

4394

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

4395

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

4397

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

4402

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

4413

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

4434

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

4439

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

5333

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

5334

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

5335

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

5336

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

5337

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

5338

\[ {} {y^{\prime }}^{2}+3 x^{2} = 8 y \]

5339

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

5340

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

5341

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

5342

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

5343

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

5344

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

5345

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

5346

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

5347

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

5348

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

5349

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

5350

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

5351

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

5352

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

5353

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

5354

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