3.8.4 Problems 301 to 400

Table 3.491: Third and higher order ode

#

ODE

Mathematica

Maple

3245

\[ {}y^{\prime \prime \prime }+8 y = 0 \]

3246

\[ {}y^{\prime \prime \prime }-8 y = 0 \]

3247

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

3248

\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \]

3249

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y = 0 \]

3250

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

3251

\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y = 0 \]

3252

\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime } = 0 \]

3253

\[ {}y^{\left (6\right )}-64 y = 0 \]

3259

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

3260

\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = \sin \left (2 x \right ) {\mathrm e}^{2 x}+2 x^{2} \]

3261

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

3262

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

3263

\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = \sin \left (x \right ) \cos \left (2 x \right ) \]

4577

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0 \]

4578

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

4579

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

4580

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

4583

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

4585

\[ {}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \]

4586

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

4588

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

4589

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

4590

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

4591

\[ {}36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

4592

\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0 \]

4595

\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0 \]

4597

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

4598

\[ {}y^{\prime \prime \prime }+8 y = 0 \]

4599

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

4600

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

4605

\[ {}3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \]

4803

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

4804

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

4805

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y = 0 \]

4806

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

4866

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

4885

\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0 \]

5046

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

5048

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

5049

\[ {}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \]

5169

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

5183

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

5184

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

5185

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

5191

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

5211

\[ {}y^{\prime \prime \prime }-y = 5 \]

5212

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

5213

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

5349

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

5353

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

5359

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

5361

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0 \]

5364

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y = 0 \]

5365

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

5366

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

5367

\[ {}y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0 \]

5370

\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = 5 \]

5371

\[ {}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 5 \]

5372

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

5389

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

5391

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y = 2 x^{2}-4 x -1+2 x^{2} {\mathrm e}^{2 x}+5 \,{\mathrm e}^{2 x} x +{\mathrm e}^{2 x} \]

5395

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

5396

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

5399

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

5408

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

5409

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

5432

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

5436

\[ {}\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \]

5437

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

5440

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

5441

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

5442

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

5817

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

5820

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

5858

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

5861

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 4 \,{\mathrm e}^{t} \]

5862

\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \]

5863

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = g \left (t \right ) \]

5864

\[ {}y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t} = 0 \]

5866

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

5871

\[ {}y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]

5885

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

5886

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

5914

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

5972

\[ {}y^{\prime \prime \prime }-8 y = 0 \]

5973

\[ {}y^{\prime \prime \prime \prime }+16 y = 0 \]

5974

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0 \]

5975

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

5976

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

5977

\[ {}y^{\prime \prime \prime \prime }-16 y = 0 \]

5978

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

5979

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

5980

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

5981

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

5984

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

5985

\[ {}y^{\left (5\right )}+2 y = 0 \]

5986

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

5987

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

5988

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