3.19.2 Problems 101 to 200

Table 3.721: Third and higher order non-homogeneous ODE

#

ODE

Mathematica

Maple

2163

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

2165

\[ {}y^{\prime \prime \prime \prime }+4 y = 5 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]

2182

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

2183

\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }-5 y^{\prime } = {\mathrm e}^{3 x} \]

2186

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

2187

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

2188

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

2196

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

2200

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

2210

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

2211

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

2212

\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right ) \]

2220

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

2221

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

2222

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

2223

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

2224

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

2225

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+9 y^{\prime \prime } = \sin \left (3 x \right )+x \,{\mathrm e}^{x} \]

2226

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

2227

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

2228

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

2229

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

2230

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

2231

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

2232

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

2233

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

2237

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

2238

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

2240

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

2241

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

2242

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

2258

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

2262

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

2263

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

2264

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

2265

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

2520

\[ {}y^{\prime \prime \prime }-12 y^{\prime }+16 y = 32 x -8 \]

2527

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

2528

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

2617

\[ {}y^{\prime \prime \prime } = 6 x \]

2742

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

2743

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }+8 y = 24 \,{\mathrm e}^{-3 x} \]

2744

\[ {}y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = 6 \,{\mathrm e}^{-x} \]

2750

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 4 x^{2} \]

2751

\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 9 \,{\mathrm e}^{-x} \]

2752

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

2759

\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y = 4 x \,{\mathrm e}^{x} \]

2760

\[ {}y^{\prime \prime \prime \prime }+104 y^{\prime \prime \prime }+2740 y^{\prime \prime } = 5 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \]

2792

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

2793

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \]

2794

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

2795

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 12 \,{\mathrm e}^{3 x} \]

2828

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = x^{2} \]

2829

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = \sin \left (4 x \right ) \]

2830

\[ {}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1 \]

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

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

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

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

5213

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

5353

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

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

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

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

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

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

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

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

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

5914

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

5991

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

5992

\[ {}y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \]

5993

\[ {}y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right ) \]

5994

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \]

5995

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

6004

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

6005

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

6316

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

6364

\[ {}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \]

6365

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \]

6366

\[ {}y^{\prime \prime \prime }-y^{\prime } = 1 \]