2.2.224 Problems 22301 to 22400

Table 2.461: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

22301

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.043

22302

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y&=2 x^{2} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

3.159

22303

\begin{align*} y+\left (2 x -3 y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

21.638

22304

\begin{align*} y^{\prime }&=3 \sin \left (x \right ) \\ y \left (\pi \right ) &= -1 \\ \end{align*}

[_quadrature]

0.348

22305

\begin{align*} x^{\prime }&=4 \,{\mathrm e}^{-t}-2 \\ x \left (0\right ) &= 3 \\ \end{align*}

[_quadrature]

0.378

22306

\begin{align*} x^{\prime \prime }&=t^{2}-4 t +8 \\ x \left (0\right ) &= 1 \\ x^{\prime }\left (0\right ) &= -3 \\ \end{align*}

[[_2nd_order, _quadrature]]

2.094

22307

\begin{align*} s^{\prime }&=9 \sqrt {u} \\ s \left (4\right ) &= 16 \\ \end{align*}

[_quadrature]

0.704

22308

\begin{align*} y^{\prime \prime }&=12 x \left (4-x \right ) \\ y \left (0\right ) &= 7 \\ y \left (1\right ) &= 0 \\ \end{align*}

[[_2nd_order, _quadrature]]

2.423

22309

\begin{align*} y^{\prime }&=-\frac {4}{x^{2}} \\ y \left (1\right ) &= 2 \\ \end{align*}

[_quadrature]

0.561

22310

\begin{align*} y^{\prime \prime }&=1-\cos \left (x \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

[[_2nd_order, _quadrature]]

1.457

22311

\begin{align*} y^{\prime \prime }&=\sqrt {2 x +1} \\ y \left (0\right ) &= 5 \\ y \left (4\right ) &= -3 \\ \end{align*}

[[_2nd_order, _quadrature]]

21.014

22312

\begin{align*} y^{\prime }-2 y&=0 \\ \end{align*}

[_quadrature]

0.591

22313

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.659

22314

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.047

22315

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

2.534

22316

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.566

22317

\begin{align*} y^{\prime \prime }+y^{2}&=0 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

3.276

22318

\begin{align*} y^{\prime }&=2 y x +1 \\ y \left (1\right ) &= 0 \\ \end{align*}

[_linear]

1.414

22319

\begin{align*} y^{\prime }&=\frac {-x +3}{y+5} \\ \end{align*}

[_separable]

3.787

22320

\begin{align*} y^{\prime \prime \prime }&=-24 \cos \left (\frac {\pi x}{2}\right ) \\ y \left (0\right ) &= -4 \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 6 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.148

22321

\begin{align*} x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

0.428

22322

\begin{align*} y^{\prime }&=y \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

0.746

22323

\begin{align*} y^{\prime }&={\mathrm e}^{y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

0.677

22324

\begin{align*} y^{\prime }&=\sec \left (y\right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

1.029

22325

\begin{align*} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

1.867

22326

\begin{align*} y^{\prime }+\tan \left (x \right ) y&=0 \\ y \left (\pi \right ) &= 4 \\ \end{align*}

[_separable]

2.187

22327

\begin{align*} y^{\prime \prime }-y&=4 x \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

24.783

22328

\begin{align*} y^{\prime }&=\frac {x +y}{-x +y} \\ y \left (-2\right ) &= 3 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7.410

22329

\begin{align*} y^{\prime \prime \prime }&=0 \\ y \left (0\right ) &= 1 \\ y \left (1\right ) &= 2 \\ y \left (2\right ) &= 9 \\ \end{align*}

[[_3rd_order, _quadrature]]

0.049

22330

\begin{align*} 2 y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime }&=0 \\ y \left (3\right ) &= 1 \\ y^{\prime }\left (3\right ) &= 2 \\ \end{align*}

[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

1.314

22331

\begin{align*} y^{\prime \prime }+y&={\mathrm e}^{-x^{2}} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

[[_2nd_order, _linear, _nonhomogeneous]]

1.211

22332

\begin{align*} y^{\prime }&=y^{3} \\ \end{align*}

[_quadrature]

3.390

22333

\begin{align*} y^{\prime }&=y^{p} \\ \end{align*}

[_quadrature]

2.264

22334

\begin{align*} y^{\prime \prime }+\lambda y&=0 \\ y \left (0\right ) &= 0 \\ y \left (1\right ) &= 0 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.977

22335

\begin{align*} \left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \\ \end{align*}

[_quadrature]

0.187

22336

\begin{align*} {| y^{\prime }|}+1&=0 \\ \end{align*}

[_sym_implicit]

0.070

22337

\begin{align*} 1+{y^{\prime }}^{2}&=0 \\ \end{align*}

[_quadrature]

0.270

22338

\begin{align*} {| y^{\prime }|}+{| y|}&=0 \\ \end{align*}

[_quadrature]

2.361

22339

\begin{align*} y^{\prime }&=3 x +2 y \\ y \left (1\right ) &= 4 \\ \end{align*}

[[_linear, ‘class A‘]]

1.093

22340

\begin{align*} y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[‘y=_G(x,y’)‘]

1.598

22341

\begin{align*} y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[‘y=_G(x,y’)‘]

49.518

22342

\begin{align*} y^{\prime }+y x&=x^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_linear]

1.472

22343

\begin{align*} y^{\prime }&=\frac {x -2 y}{y-2 x} \\ y \left (1\right ) &= 2 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12.735

22344

\begin{align*} y^{\prime }&=\frac {1}{x^{2}-y^{2}} \\ y \left (1\right ) &= 2 \\ \end{align*}

[‘y=_G(x,y’)‘]

1.602

22345

\begin{align*} y^{\prime }&=x^{2}+y^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}

[[_Riccati, _special]]

12.541

22346

\begin{align*} y^{\prime }&=\sqrt {y x} \\ y \left (1\right ) &= 0 \\ \end{align*}

[[_homogeneous, ‘class G‘]]

85.724

22347

\begin{align*} y^{\prime }&=y \csc \left (x \right ) \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

3.563

22348

\begin{align*} y^{\prime }&=\frac {1}{\sqrt {x^{2}+4 y^{2}-4}} \\ y \left (3\right ) &= 2 \\ \end{align*}

[‘y=_G(x,y’)‘]

2.353

22349

\begin{align*} y^{\prime }&=\sqrt {y} \\ \end{align*}

[_quadrature]

1.467

22350

\begin{align*} y^{\prime }&=2 x -y \\ y \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

1.054

22351

\begin{align*} y^{\prime }&=2 x \\ \end{align*}

[_quadrature]

0.306

22352

\begin{align*} y^{\prime }&=\frac {y}{x} \\ \end{align*}

[_separable]

1.903

22353

\begin{align*} y^{\prime }&=x +y \\ \end{align*}

[[_linear, ‘class A‘]]

0.882

22354

\begin{align*} y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \\ \end{align*}

[‘y=_G(x,y’)‘]

1.216

22355

\begin{align*} y^{\prime }&=\sqrt {-x +y}+1 \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

1.862

22356

\begin{align*} y^{\prime \prime }+x {y^{\prime }}^{2}&=1 \\ \end{align*}

[[_2nd_order, _missing_y]]

249.887

22357

\begin{align*} y^{\prime \prime } x +y^{\prime }+y x&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

[_Lienard]

2.678

22358

\begin{align*} y^{\prime }&=\frac {\left (\sqrt {y x +1}-1\right )^{2}}{x^{2}} \\ \end{align*}

[[_homogeneous, ‘class G‘], _Clairaut]

6.675

22359

\begin{align*} y^{\prime }&=-\frac {x}{y} \\ y \left (1\right ) &= 2 \\ \end{align*}

[_separable]

5.743

22360

\begin{align*} y^{\prime }&=-\frac {y}{x} \\ y \left (1\right ) &= 3 \\ \end{align*}

[_separable]

3.788

22361

\begin{align*} 3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.890

22362

\begin{align*} 2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\ \end{align*}

[_separable]

2.565

22363

\begin{align*} y^{\prime }&=\frac {x y^{2}+x}{4 y} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_separable]

2.437

22364

\begin{align*} y^{\prime } x&=1+y^{2} \\ \end{align*}

[_separable]

2.970

22365

\begin{align*} \sin \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

3.150

22366

\begin{align*} x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\ \end{align*}

[_separable]

3.424

22367

\begin{align*} 2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 2 \\ \end{align*}

[_separable]

3.146

22368

\begin{align*} y^{\prime }&=8 y x +3 y \\ \end{align*}

[_separable]

2.228

22369

\begin{align*} i^{\prime }+5 i&=10 \\ i \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.870

22370

\begin{align*} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

3.718

22371

\begin{align*} y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\ \end{align*}

[_separable]

2.704

22372

\begin{align*} y^{\prime }&=\frac {\left (-1+y\right ) \left (3+y\right )}{\left (y-2\right ) \left (x +3\right )} \\ \end{align*}

[_separable]

8.700

22373

\begin{align*} r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\ r \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

[_separable]

5.252

22374

\begin{align*} r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\ r \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

[_separable]

4.406

22375

\begin{align*} x^{3} {\mathrm e}^{2 x^{2}+3 y^{2}}-y^{3} {\mathrm e}^{-x^{2}-2 y^{2}} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.601

22376

\begin{align*} U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

40.056

22377

\begin{align*} y^{\prime }&=\frac {4 y^{2}-x^{4}}{4 y x} \\ \end{align*}

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

4.197

22378

\begin{align*} x^{2}+y \sin \left (y x \right )+x \sin \left (y x \right ) y^{\prime }&=0 \\ \end{align*}

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

2.435

22379

\begin{align*} y^{\prime }&=1+\frac {y}{x} \\ \end{align*}

[_linear]

2.502

22380

\begin{align*} y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\ y \left (1\right ) &= 1 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

4.485

22381

\begin{align*} y^{\prime } x&=2 x +3 y \\ \end{align*}

[_linear]

3.589

22382

\begin{align*} x^{2}-y^{2}-2 y y^{\prime } x&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli]

6.401

22383

\begin{align*} x +2+\left (2 x +y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

20.473

22384

\begin{align*} y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\ y \left (1\right ) &= \frac {\pi }{4} \\ \end{align*}

[[_homogeneous, ‘class D‘]]

5.516

22385

\begin{align*} y^{\prime } x&=y-\sqrt {x^{2}+y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

11.457

22386

\begin{align*} y&=\left (2 x +3 y\right ) y^{\prime } \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

22.095

22387

\begin{align*} x^{3}+y^{3}-y^{\prime } y^{2} x&=0 \\ y \left (1\right ) &= 0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

7.569

22388

\begin{align*} y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

10.403

22389

\begin{align*} y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

4.356

22390

\begin{align*} x -4 y+\left (3 x -2\right ) y^{\prime }&=0 \\ \end{align*}

[_linear]

3.068

22391

\begin{align*} y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}}{x} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

18.531

22392

\begin{align*} y^{\prime }&=\frac {2 x +5 y}{2 x -y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13.046

22393

\begin{align*} y^{\prime }&=\frac {6 x^{2}-5 y x -2 y^{2}}{6 x^{2}-8 y x +y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

13.582

22394

\begin{align*} y^{\prime }&=\left (x +y\right )^{2} \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

1.532

22395

\begin{align*} y^{\prime }&=\sqrt {2 x +3 y} \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

3.822

22396

\begin{align*} y^{\prime }&=\frac {2 x +3 y+1}{3 x -2 y-5} \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

17.292

22397

\begin{align*} \left (3 x -y-9\right ) y^{\prime }&=10-2 x +2 y \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

47.488

22398

\begin{align*} 2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

7.530

22399

\begin{align*} 2 x +2 y+1+\left (x +y-1\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

6.313

22400

\begin{align*} 2 x \sin \left (\frac {y}{x}\right )+2 x \tan \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )-y \sec \left (\frac {y}{x}\right )^{2}+\left (x \cos \left (\frac {y}{x}\right )+x \sec \left (\frac {y}{x}\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

43.730