3.12.3 Problems 201 to 300

Table 3.661: Third and higher order linear ODE

#

ODE

Mathematica

Maple

2112

\[ {}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y = 0 \]

2113

\[ {}y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y = 0 \]

2114

\[ {}y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime } = 0 \]

2115

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

2116

\[ {}y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime } = 0 \]

2119

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

2120

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

2121

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

2122

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

2123

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

2124

\[ {}4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime } = 0 \]

2125

\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y = 0 \]

2126

\[ {}4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y = 0 \]

2127

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

2128

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

2130

\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y = 0 \]

2131

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

2132

\[ {}y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y = 0 \]

2133

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

2134

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

2135

\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y = 0 \]

2136

\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y = 0 \]

2137

\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y = 0 \]

2138

\[ {}4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y = 0 \]

2139

\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y = 0 \]

2147

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

2153

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

2155

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

2156

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

2158

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

2159

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

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

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

2528

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

2617

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

2729

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

2730

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y = 0 \]

2731

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-18 y^{\prime }-40 y = 0 \]

2732

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

2733

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

2734

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

2735

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

2738

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

2739

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

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

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

2824

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

2825

\[ {}y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y = 0 \]

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

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

3242

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

3243

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

3244

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

3245

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