2.2.174 Problems 17301 to 17400

Table 2.361: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

17301

\begin{align*} 1+y-y^{\prime } t&=\ln \left (y^{\prime }\right ) \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

16.930

17302

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

1.716

17303

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

[_dAlembert]

0.678

17304

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

[_dAlembert]

14.051

17305

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

[_linear]

4.749

17306

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

1.679

17307

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

[[_homogeneous, ‘class G‘], _rational]

46.856

17308

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

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

21.996

17309

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

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

26.779

17310

\begin{align*} y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\ \end{align*}

[_separable]

15.671

17311

\begin{align*} \cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right )&=0 \\ \end{align*}

[_separable]

4.735

17312

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

[_separable]

5.578

17313

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\ \end{align*}

[_separable]

4.382

17314

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\ \end{align*}

[_separable]

6.458

17315

\begin{align*} -\frac {1}{x^{5}}+\frac {1}{x^{3}}&=\left (2 y^{4}-6 y^{9}\right ) y^{\prime } \\ \end{align*}

[_separable]

4.013

17316

\begin{align*} y^{\prime }&=\frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \\ \end{align*}

[_separable]

5.087

17317

\begin{align*} y^{\prime }&=\frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \\ \end{align*}

[_separable]

6.456

17318

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

[[_linear, ‘class A‘]]

2.762

17319

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

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

34.971

17320

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

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

21.812

17321

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

[[_linear, ‘class A‘]]

2.392

17322

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

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

148.625

17323

\begin{align*} r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\ \end{align*}

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

22.316

17324

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

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

56.277

17325

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

[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]

3.449

17326

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

[_exact]

6.563

17327

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

[_exact]

4.991

17328

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

7.010

17329

\begin{align*} y+y^{\prime }&=5 \\ \end{align*}

[_quadrature]

1.141

17330

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

[_separable]

4.460

17331

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

[_linear]

5.449

17332

\begin{align*} t r^{\prime }+r&=t \cos \left (t \right ) \\ \end{align*}

[_linear]

2.784

17333

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

[_Bernoulli]

16.655

17334

\begin{align*} y+y^{\prime }&=\frac {{\mathrm e}^{t}}{y^{2}} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Bernoulli]

4.554

17335

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

4.862

17336

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

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

21.749

17337

\begin{align*} y-y^{\prime } t&=-2 {y^{\prime }}^{3} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.689

17338

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.390

17339

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

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

19.069

17340

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

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

16.625

17341

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

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

4.242

17342

\begin{align*} \sin \left (y\right )-y \cos \left (t \right )+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime }&=0 \\ y \left (\pi \right ) &= 0 \\ \end{align*}

[_exact]

13.651

17343

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

6.056

17344

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

[_exact]

7.199

17345

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

[[_Riccati, _special]]

707.825

17346

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

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

18.441

17347

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

[_separable]

46.386

17348

\begin{align*} y^{\prime }&=\frac {t}{y^{3}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

50.898

17349

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

[_separable]

4.701

17350

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

[[_2nd_order, _missing_x]]

5.240

17351

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

[[_2nd_order, _missing_x]]

5.863

17352

\begin{align*} 2 t^{2} y^{\prime \prime }-3 y^{\prime } t -3 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

3.920

17353

\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.799

17354

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

[[_2nd_order, _missing_x]]

1.027

17355

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -3 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.419

17356

\begin{align*} 3 t^{2} y^{\prime \prime }-5 y^{\prime } t -3 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= {\frac {17}{3}} \\ \end{align*}

[[_Emden, _Fowler]]

8.635

17357

\begin{align*} t^{2} y^{\prime \prime }+7 y^{\prime } t -7 y&=0 \\ y \left (1\right ) &= 2 \\ y^{\prime }\left (1\right ) &= -22 \\ \end{align*}

[[_Emden, _Fowler]]

7.907

17358

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

[[_2nd_order, _linear, _nonhomogeneous]]

1.563

17359

\begin{align*} y^{\prime \prime }+10 y^{\prime }+24 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.615

17360

\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.466

17361

\begin{align*} y^{\prime \prime }+6 y^{\prime }+18 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

9.029

17362

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

[[_2nd_order, _exact, _linear, _homogeneous]]

4.542

17363

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

[[_2nd_order, _missing_x]]

0.185

17364

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.196

17365

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

[[_2nd_order, _missing_x]]

0.311

17366

\begin{align*} y^{\prime \prime }+10 y^{\prime }+25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.197

17367

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -4 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.356

17368

\begin{align*} y^{\prime \prime }+49 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.199

17369

\begin{align*} t^{2} y^{\prime \prime }+4 y^{\prime } t -4 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.162

17370

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

[[_Emden, _Fowler]]

0.165

17371

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

[[_2nd_order, _with_linear_symmetries]]

0.180

17372

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \\ \end{align*}

[[_2nd_order, _exact, _linear, _homogeneous]]

0.162

17373

\begin{align*} a y^{\prime \prime }+b y^{\prime }+c y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

28.785

17374

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

[[_Emden, _Fowler]]

18.866

17375

\begin{align*} 4 t^{2} y^{\prime \prime }+4 y^{\prime } t +\left (36 t^{2}-1\right ) y&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.198

17376

\begin{align*} t y^{\prime \prime }+2 y^{\prime }+16 t y&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.186

17377

\begin{align*} y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y&=0 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.765

17378

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

[[_2nd_order, _missing_x]]

0.954

17379

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

[[_2nd_order, _quadrature]]

1.519

17380

\begin{align*} y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.259

17381

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

[[_2nd_order, _missing_x]]

3.691

17382

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

[[_2nd_order, _missing_x]]

7.236

17383

\begin{align*} y^{\prime \prime }+8 y^{\prime }+12 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.436

17384

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

[[_2nd_order, _missing_x]]

9.777

17385

\begin{align*} 8 y^{\prime \prime }+6 y^{\prime }+y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.502

17386

\begin{align*} 4 y^{\prime \prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.398

17387

\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

3.649

17388

\begin{align*} y^{\prime \prime }+8 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.055

17389

\begin{align*} y^{\prime \prime }+7 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.840

17390

\begin{align*} 4 y^{\prime \prime }+21 y^{\prime }+5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

8.459

17391

\begin{align*} 7 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.207

17392

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

[[_2nd_order, _missing_x]]

6.309

17393

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.322

17394

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

[[_2nd_order, _missing_x]]

2.240

17395

\begin{align*} 3 y^{\prime \prime }-y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

[[_2nd_order, _missing_x]]

2.985

17396

\begin{align*} y^{\prime \prime }+y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.663

17397

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.008

17398

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.969

17399

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.981

17400

\begin{align*} y^{\prime \prime }+36 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= -6 \\ \end{align*}

[[_2nd_order, _missing_x]]

7.262