3.26.11 Problems 1001 to 1100

Table 3.909: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

8205

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

8206

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

8207

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

8208

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

8209

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

8210

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

8211

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

8212

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

8213

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

8214

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

8215

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

8216

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

8217

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

8218

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

8219

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

8220

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

8221

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

8222

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

8223

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

8224

\[ {}2 x^{2} \left (2-x \right ) y^{\prime \prime }-x \left (4-x \right ) y^{\prime }+\left (3-x \right ) y = 0 \]

8225

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \]

8226

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

8227

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

8228

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

8229

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+12 y = 0 \]

8230

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

8231

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

8232

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

8233

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

8234

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

8235

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

8236

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

8237

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

8238

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \]

8239

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

8240

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

8241

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

8242

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

8243

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

8244

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

8245

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

8246

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

8247

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

8248

\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \]

8249

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

8250

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

8251

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

8252

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

8253

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

8254

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

8255

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

8256

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

8257

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

8258

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

8259

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

8260

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

8261

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]

8262

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

8263

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

8264

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

8265

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

8266

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

8267

\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+\left (4 x^{2}+6\right ) y = 0 \]

8268

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

8269

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

8270

\[ {}4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y = 0 \]

8271

\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]

8272

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

8273

\[ {}x^{2} y^{\prime \prime }+\frac {\left (x +\frac {3}{4}\right ) y}{4} = 0 \]

8274

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

8275

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

8276

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

8277

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

8278

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

8279

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

8280

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

8281

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

8283

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

8284

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

8285

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

8286

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

8287

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

8288

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

8289

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

8290

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

8291

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

8292

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

8293

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

8294

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

8295

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

8296

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

8297

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

8298

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

8299

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

8300

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

8301

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

8302

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

8303

\[ {}x^{2} \left (x^{2}-2 x +1\right ) y^{\prime \prime }-x \left (x +3\right ) y^{\prime }+\left (x +4\right ) y = 0 \]

8304

\[ {}2 x^{2} \left (2+x \right ) y^{\prime \prime }+5 x^{2} y^{\prime }+\left (1+x \right ) y = 0 \]

8305

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