4.4.13 Problems 1201 to 1300

Table 4.569: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

6606

\[ {} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0 \]

6607

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

6608

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

6609

\[ {} f \left (y^{\prime \prime }, y^{\prime }-x y^{\prime \prime }, y-x y^{\prime }+\frac {x^{2} y^{\prime \prime }}{2}\right ) = 0 \]

6812

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

7051

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

7052

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

7053

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

7054

\[ {} 6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]

7055

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

7060

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

7061

\[ {} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]

7063

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

7066

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

7072

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

7073

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

7075

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

7080

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

7081

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

7082

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

7083

\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]

7130

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

7135

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

7136

\[ {} r^{\prime \prime } = -\frac {k}{r^{2}} \]

7137

\[ {} y^{\prime \prime } = \frac {3 k y^{2}}{2} \]

7138

\[ {} y^{\prime \prime } = 2 k y^{3} \]

7139

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

7140

\[ {} r^{\prime \prime } = \frac {h^{2}}{r^{3}}-\frac {k}{r^{2}} \]

7141

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

7142

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

7144

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

7145

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

7146

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

7147

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

7148

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

7151

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

7152

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

7153

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

7161

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

7165

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

7211

\[ {} u^{\prime \prime }-\frac {a^{2} u}{x^{{2}/{3}}} = 0 \]

7212

\[ {} u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \]

7213

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

7214

\[ {} u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \]

7215

\[ {} u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]

7216

\[ {} u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

7217

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

7218

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

7219

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \]

7220

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \]

7221

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

7222

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

7223

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

7224

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

7225

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

7226

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

7270

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

7271

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

7272

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

7273

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

7274

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

7275

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

7276

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

7277

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

7278

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

7279

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

7280

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

7281

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

7318

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

7319

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

7320

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

7321

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

7322

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

7323

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

7324

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

7325

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

7327

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

7328

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

7329

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

7330

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

7337

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

7338

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

7339

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

7340

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

7341

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

7342

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

7346

\[ {} r^{\prime \prime }-6 r^{\prime }+9 r = 0 \]

7366

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

7378

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

7380

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

7382

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

7384

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

7386

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

7388

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

7390

\[ {} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y = 0 \]

7581

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

7582

\[ {} m y^{\prime \prime }+b y^{\prime }+k y = 0 \]

7583

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

7584

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

7585

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