5.12.4 Problems 301 to 400

Table 5.825: Third and higher order linear ODE

#

ODE

Mathematica

Maple

3099

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

3101

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

3102

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

3103

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

3104

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

3105

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

3106

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

3107

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

3108

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

3109

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

3110

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

3118

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

3124

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

3126

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

3127

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

3129

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

3130

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

3134

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

3136

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

3153

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

3154

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

3157

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

3158

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

3159

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

3167

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

3171

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

3181

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

3182

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

3183

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

3191

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

3192

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

3193

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

3194

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

3195

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

3196

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

3197

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

3198

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

3199

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

3200

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

3201

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

3202

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

3203

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

3204

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

3208

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

3209

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

3211

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

3212

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

3213

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

3229

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

3233

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

3234

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

3235

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

3236

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

3491

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

3499

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

3588

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

3700

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

3701

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

3702

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

3703

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

3704

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

3705

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

3706

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

3709

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

3710

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

3713

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

3714

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

3715

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

3721

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

3722

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

3723

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

3730

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

3731

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

3763

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

3764

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

3765

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

3766

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

3795

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

3796

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

3799

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

3800

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

3801

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

4142

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

4143

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

4144

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

4145

\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y = 0 \]

4146

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

4147

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

4148

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

4149

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

4150

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

4151

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

4159

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

4160

\[ {}y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y = \cos \left (2 x +3\right ) \]

4165

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

4414

\[ {}y^{\prime \prime \prime } = 2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \]

4444

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

4445

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

4446

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

4447

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