4.5.9 Problems 801 to 900

Table 4.665: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

6584

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

6586

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

6588

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

6589

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

6590

\[ {} h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime } = 0 \]

6591

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

6592

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

6595

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

6596

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

7085

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

7086

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

7087

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

7088

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

7089

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

7090

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]

7091

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

7092

\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 9 x \,{\mathrm e}^{x}+10 \,{\mathrm e}^{-x} \]

7093

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

7094

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

7095

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

7096

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

7097

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

7098

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

7099

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

7100

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

7101

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

7102

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

7103

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

7104

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

7105

\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \]

7106

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

7107

\[ {} y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \]

7108

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \]

7109

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

7110

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

7111

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

7112

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

7113

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

7114

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

7115

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

7116

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

7117

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

7118

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

7119

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

7120

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

7121

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

7122

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

7123

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

7124

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

7125

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

7126

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

7127

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

7128

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

7129

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

7131

\[ {} y^{3} y^{\prime \prime } = k \]

7132

\[ {} y y^{\prime \prime } = {y^{\prime }}^{2}-1 \]

7133

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

7134

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

7143

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

7149

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

7150

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

7286

\[ {} y^{\prime \prime }-4 y^{\prime } = 10 \]

7287

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

7288

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

7289

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 24 \,{\mathrm e}^{-3 x} \]

7290

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

7291

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

7292

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

7293

\[ {} y^{\prime \prime }-16 y = 40 \,{\mathrm e}^{4 x} \]

7294

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

7295

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

7296

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 100 \cos \left (4 x \right ) \]

7297

\[ {} y^{\prime \prime }+4 y^{\prime }+12 y = 80 \sin \left (2 x \right ) \]

7298

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

7299

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 120 \sin \left (5 x \right ) \]

7300

\[ {} 5 y^{\prime \prime }+12 y^{\prime }+20 y = 120 \sin \left (2 x \right ) \]

7301

\[ {} y^{\prime \prime }+9 y = 30 \sin \left (3 x \right ) \]

7302

\[ {} y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]

7303

\[ {} y^{\prime \prime }+2 y^{\prime }+17 y = 60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \]

7304

\[ {} 4 y^{\prime \prime }+4 y^{\prime }+5 y = 40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \]

7305

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = 30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \]

7306

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

7307

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

7308

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

7309

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

7310

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 16 x^{2} {\mathrm e}^{-x} \]

7311

\[ {} y^{\prime \prime }+y = 8 x \sin \left (x \right ) \]

7312

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

7313

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{x}+6 x -5 \]

7314

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

7315

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

7316

\[ {} y+2 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{x}+\left (1-x \right ) \left ({\mathrm e}^{2 x}-1\right ) \]

7317

\[ {} y^{\prime \prime }-2 y^{\prime } = 9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \]

7326

\[ {} k = \frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{{3}/{2}}} \]

7331

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4} \]

7332

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

7333

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3} \]

7334

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

7335

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

7336

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