2.5.2 higher order Euler ode

Table 2.505: higher order Euler ode

#

ODE

CAS classification

Solved?

255

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

256

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

314

\[ {}a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

317

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0 \]

[[_3rd_order, _missing_y]]

318

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

[[_3rd_order, _missing_y]]

319

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

[[_3rd_order, _missing_y]]

320

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

[[_3rd_order, _missing_y]]

321

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \]

[[_3rd_order, _exact, _linear, _homogeneous]]

958

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0 \]

[[_3rd_order, _missing_y]]

959

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

[[_3rd_order, _missing_y]]

960

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

[[_3rd_order, _missing_y]]

961

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

[[_3rd_order, _missing_y]]

962

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \]

[[_3rd_order, _exact, _linear, _homogeneous]]

1467

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

[[_3rd_order, _exact, _linear, _homogeneous]]

2107

\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]
i.c.

[[_3rd_order, _exact, _linear, _homogeneous]]

2109

\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]
i.c.

[[_3rd_order, _exact, _linear, _homogeneous]]

2110

\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]
i.c.

[[_3rd_order, _exact, _linear, _homogeneous]]

2111

\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]
i.c.

[[_3rd_order, _exact, _linear, _homogeneous]]

2112

\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \]
i.c.

[[_3rd_order, _exact, _linear, _homogeneous]]

2222

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 2 x \]

[[_3rd_order, _with_linear_symmetries]]

2223

\[ {}4 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-5 x y^{\prime }+2 y = 30 x^{2} \]

[[_3rd_order, _with_linear_symmetries]]

2224

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

2225

\[ {}16 x^{4} y^{\prime \prime \prime \prime }+96 x^{3} y^{\prime \prime \prime }+72 x^{2} y^{\prime \prime }-24 x y^{\prime }+9 y = 96 x^{{5}/{2}} \]

[[_high_order, _with_linear_symmetries]]

2226

\[ {}x^{4} y^{\prime \prime \prime \prime }-4 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }-24 x y^{\prime }+24 y = x^{4} \]

[[_high_order, _with_linear_symmetries]]

2227

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 12 x^{2} \]

[[_high_order, _exact, _linear, _nonhomogeneous]]

2228

\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 4 x \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

2229

\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = x^{3} \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

2230

\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+16 x y^{\prime }-16 y = 9 x^{4} \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

2231

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

2232

\[ {}x^{4} y^{\prime \prime \prime \prime }+3 x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 9 x^{2} \]
i.c.

[[_high_order, _exact, _linear, _nonhomogeneous]]

2233

\[ {}4 x^{4} y^{\prime \prime \prime \prime }+24 x^{3} y^{\prime \prime \prime }+23 x^{2} y^{\prime \prime }-x y^{\prime }+y = 6 x \]
i.c.

[[_high_order, _exact, _linear, _nonhomogeneous]]

2234

\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-6 x y^{\prime }+6 y = 40 x^{3} \]
i.c.

[[_high_order, _exact, _linear, _nonhomogeneous]]

2236

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

2238

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = F \left (x \right ) \]

[[_high_order, _exact, _linear, _nonhomogeneous]]

3229

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

3233

\[ {}4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y = x +\ln \left (x \right ) \]

[[_3rd_order, _with_linear_symmetries]]

3234

\[ {}3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 x y^{\prime }+10 y = \frac {4}{x^{2}} \]

[[_3rd_order, _with_linear_symmetries]]

3235

\[ {}x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 x y^{\prime }-6 y = \cos \left (\ln \left (x \right )\right ) \]

[[_high_order, _exact, _linear, _nonhomogeneous]]

3236

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

[[_3rd_order, _linear, _nonhomogeneous]]

3709

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

[[_3rd_order, _exact, _linear, _homogeneous]]

3710

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

[[_3rd_order, _missing_y]]

4165

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

[[_3rd_order, _exact, _linear, _homogeneous]]

4511

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

4513

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

[[_3rd_order, _with_linear_symmetries]]

6696

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

[[_3rd_order, _with_linear_symmetries]]

6751

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

[[_3rd_order, _missing_y]]

6752

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

[[_3rd_order, _with_linear_symmetries]]

6899

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 12 x^{2} \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

6932

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

7488

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

[[_high_order, _with_linear_symmetries]]

7683

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

[[_3rd_order, _with_linear_symmetries]]

7703

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

[[_3rd_order, _exact, _linear, _homogeneous]]

8035

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

[[_3rd_order, _missing_y]]

8036

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

[[_3rd_order, _exact, _linear, _homogeneous]]

8037

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

[[_3rd_order, _with_linear_symmetries]]

8615

\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

8876

\[ {}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

8877

\[ {}x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+x y = x \]

[[_3rd_order, _with_linear_symmetries]]

8878

\[ {}5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+x^{2} y^{\prime }+x y = 0 \]

[[_high_order, _with_linear_symmetries]]

11458

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

[[_3rd_order, _with_linear_symmetries]]

11476

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-6 x^{3} \left (-1+x \right ) \ln \left (x \right )+x^{3} \left (x +8\right ) = 0 \]

[[_3rd_order, _with_linear_symmetries]]

11479

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+\left (a \,x^{3}-12\right ) y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

11482

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

[[_3rd_order, _linear, _nonhomogeneous]]

11527

\[ {}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime } = 0 \]

[[_high_order, _missing_y]]

11528

\[ {}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+12 x^{2} y^{\prime \prime }+a y = 0 \]

[[_high_order, _with_linear_symmetries]]

12869

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

[[_3rd_order, _with_linear_symmetries]]

12870

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x} \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

12878

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (1+\ln \left (x \right )\right )^{2} \]

[[_high_order, _linear, _nonhomogeneous]]

12884

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

13178

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

[[_3rd_order, _fully, _exact, _linear]]

13189

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

13319

\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

13462

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

[[_3rd_order, _with_linear_symmetries]]

13463

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0 \]

[[_3rd_order, _fully, _exact, _linear]]

13464

\[ {}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-6 x y^{\prime }+18 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

13470

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

[[_3rd_order, _with_linear_symmetries]]

13584

\[ {}t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x = 0 \]

[[_3rd_order, _with_linear_symmetries]]

14265

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

[[_3rd_order, _with_linear_symmetries]]

15324

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

[[_3rd_order, _with_linear_symmetries]]

15325

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

[[_3rd_order, _with_linear_symmetries]]

15326

\[ {}x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

15327

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

15328

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 x y^{\prime }+16 y = 0 \]

[[_high_order, _with_linear_symmetries]]

15329

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 0 \]

[[_high_order, _exact, _linear, _homogeneous]]

15330

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

[[_high_order, _with_linear_symmetries]]

15331

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

[[_high_order, _exact, _linear, _homogeneous]]

15451

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3} \]

[[_3rd_order, _with_linear_symmetries]]

15452

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = {\mathrm e}^{-x^{2}} \]

[[_3rd_order, _with_linear_symmetries]]

15455

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 12 x \sin \left (x^{2}\right ) \]

[[_high_order, _exact, _linear, _nonhomogeneous]]

16359

\[ {}2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+t y^{\prime }-y = -3 t^{2} \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

16373

\[ {}x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 x y^{\prime }+140 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

16374

\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 x y^{\prime }+100 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

16375

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

[[_3rd_order, _with_linear_symmetries]]

16376

\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

[[_3rd_order, _exact, _linear, _homogeneous]]

16377

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

[[_3rd_order, _with_linear_symmetries]]

16378

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

[[_3rd_order, _exact, _linear, _homogeneous]]

16379

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \]

[[_3rd_order, _exact, _linear, _homogeneous]]

16389

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y = \frac {1}{x^{3}} \]

[[_3rd_order, _with_linear_symmetries]]

16390

\[ {}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 x y^{\prime }+80 y = \frac {1}{x^{13}} \]

[[_3rd_order, _with_linear_symmetries]]

16395

\[ {}x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 x y^{\prime }+20 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

16396

\[ {}x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 x y^{\prime }+42 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

16397

\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 x y^{\prime }-5 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

16398

\[ {}x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 x y^{\prime }-17 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

16406

\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime } = 0 \]

[[_3rd_order, _missing_y]]

16407

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

[[_3rd_order, _missing_y]]

16408

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

[[_3rd_order, _with_linear_symmetries]]

16409

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

[[_3rd_order, _missing_y]]

16421

\[ {}x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

16422

\[ {}x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y = 0 \]

[[_high_order, _with_linear_symmetries]]

16423

\[ {}x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y = 0 \]

[[_high_order, _exact, _linear, _homogeneous]]

16424

\[ {}x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y = 0 \]

[[_high_order, _with_linear_symmetries]]

16425

\[ {}x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 x y^{\prime }+4 y = 0 \]

[[_high_order, _with_linear_symmetries]]

16426

\[ {}x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y = 0 \]
i.c.

[[_3rd_order, _with_linear_symmetries]]

17734

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

[[_3rd_order, _exact, _linear, _homogeneous]]

17914

\[ {}2 x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+12 x y^{\prime }-12 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

17915

\[ {}y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}} = 0 \]

[[_3rd_order, _fully, _exact, _linear]]

17919

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

[[_3rd_order, _with_linear_symmetries]]

17951

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

[[_3rd_order, _with_linear_symmetries]]

18297

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

[[_3rd_order, _missing_y]]

18298

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

[[_3rd_order, _exact, _linear, _homogeneous]]

18299

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

[[_3rd_order, _with_linear_symmetries]]

18511

\[ {}x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime } = 17 x^{6} \]

[[_high_order, _missing_y]]

18512

\[ {}t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x = \cos \left (3 \ln \left (t \right )\right ) \]

[[_high_order, _exact, _linear, _nonhomogeneous]]

18519

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

[[_3rd_order, _with_linear_symmetries]]

18538

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

[[_3rd_order, _with_linear_symmetries]]

18605

\[ {}x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+8 x y^{\prime } = \ln \left (x \right )^{2} \]

[[_3rd_order, _missing_y]]

18607

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3} \]

[[_3rd_order, _with_linear_symmetries]]

18608

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

[[_3rd_order, _with_linear_symmetries]]

18609

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

[[_3rd_order, _exact, _linear, _homogeneous]]

18846

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

[[_3rd_order, _exact, _linear, _homogeneous]]

18847

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

[[_high_order, _with_linear_symmetries]]

18854

\[ {}y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

18856

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

18858

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

18859

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 c +\frac {10}{x} \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

18863

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (1+\ln \left (x \right )\right )^{2} \]

[[_high_order, _linear, _nonhomogeneous]]

18864

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

[[_3rd_order, _with_linear_symmetries]]

19238

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

[[_3rd_order, _exact, _linear, _homogeneous]]

19240

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

[[_3rd_order, _with_linear_symmetries]]

19241

\[ {}y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

19243

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

19257

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 4 x \]

[[_high_order, _with_linear_symmetries]]

19258

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

19260

\[ {}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y = x^{2}+\frac {1}{x^{2}} \]

[[_3rd_order, _reducible, _mu_y2]]

19261

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

[[_high_order, _with_linear_symmetries]]

19264

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

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

19265

\[ {}x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \left (1+\ln \left (x \right )\right )^{2} \]

[[_high_order, _linear, _nonhomogeneous]]

19271

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]

19290

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

[[_3rd_order, _quadrature]]

19335

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

[[_3rd_order, _with_linear_symmetries]]

19363

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

[[_3rd_order, _exact, _linear, _homogeneous]]

19499

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

[[_3rd_order, _with_linear_symmetries]]

19501

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

[[_3rd_order, _with_linear_symmetries]]

19502

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime }-4 y = 0 \]

[[_3rd_order, _with_linear_symmetries]]

19503

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

[[_3rd_order, _exact, _linear, _homogeneous]]

19505

\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y = 10 x +\frac {10}{x} \]

[[_3rd_order, _exact, _linear, _nonhomogeneous]]