5.3.5 Problems 401 to 500

Table 5.43: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

2931

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

2932

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

2933

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

2935

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

2936

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

2938

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

2945

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

2949

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

2956

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

2957

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

2964

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

2972

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

2997

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

3002

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

3003

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

3009

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

3013

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

3018

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

3024

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

3029

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

3034

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

3035

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

3037

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

3040

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

3043

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

3054

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

3056

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

3160

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

3199

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

3242

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

3247

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

3258

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

3260

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

3262

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

3264

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

3265

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

3267

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

3268

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

3269

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

3271

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

3273

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

3274

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

3275

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

3276

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

3278

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

3279

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

3280

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

3281

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

3283

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

3287

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

3290

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

3292

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

3298

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

3305

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

3307

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

3313

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

3314

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

3316

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

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

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

3326

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

3329

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

3330

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

3332

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

3333

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

3344

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

3345

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

3346

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

3347

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

3348

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

3349

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

3350

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

3361

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

3371

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

3385

\[ {} x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y = 0 \]

3388

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

3389

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

3390

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

3391

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

3392

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

3393

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

3394

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

3395

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

3396

\[ {} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y = x^{4}+x^{2} \]

3397

\[ {} 9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y = x -1 \]

3398

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

3399

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

3400

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

3401

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

3402

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

3462

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

3463

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

3465

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

3476

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

3481

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

3492

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