3.7.2 Problems 101 to 200

Table 3.455: Solved using series method

#

ODE

Mathematica

Maple

1196

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

1197

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

1198

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

1199

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

1200

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

1201

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

1202

\[ {}x^{2} \left (3 x +1\right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y = 0 \]

1203

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

1204

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

1205

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

1206

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

1207

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y = 0 \]

1208

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y = 0 \]

1209

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

1210

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

1211

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

1212

\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y = 0 \]

1213

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

1214

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

1215

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

1216

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

1217

\[ {}\left (8 x^{2}+1\right ) y^{\prime \prime }+2 y = 0 \]

1218

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

1219

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

1220

\[ {}\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (-1+x \right ) y^{\prime }+6 y = 0 \]

1221

\[ {}\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y = 0 \]

1222

\[ {}\left (3 x^{2}+6 x +5\right ) y^{\prime \prime }+9 \left (1+x \right ) y^{\prime }+3 y = 0 \]

1223

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

1224

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

1225

\[ {}\left (3 x^{2}-6 x +5\right ) y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+12 y = 0 \]

1226

\[ {}\left (4 x^{2}-24 x +37\right ) y^{\prime \prime }+y = 0 \]

1227

\[ {}\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y = 0 \]

1228

\[ {}\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (1+x \right ) y^{\prime }+60 y = 0 \]

1229

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

1230

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

1231

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

1232

\[ {}\left (-2 x^{3}+1\right ) y^{\prime \prime }-10 x^{2} y^{\prime }-8 x y = 0 \]

1233

\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 x y = 0 \]

1234

\[ {}\left (-2 x^{3}+1\right ) y^{\prime \prime }+6 x^{2} y^{\prime }+24 x y = 0 \]

1235

\[ {}\left (-x^{3}+1\right ) y^{\prime \prime }+15 x^{2} y^{\prime }-36 x y = 0 \]

1236

\[ {}\left (2 x^{5}+1\right ) y^{\prime \prime }+14 x^{4} y^{\prime }+10 x^{3} y = 0 \]

1237

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

1238

\[ {}y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y = 0 \]

1239

\[ {}\left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y = 0 \]

1240

\[ {}\left (-x^{6}+1\right ) y^{\prime \prime }-12 x^{5} y^{\prime }-30 x^{4} y = 0 \]

1241

\[ {}y^{\prime \prime }+x^{5} y^{\prime }+6 x^{4} y = 0 \]

1242

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

1243

\[ {}\left (2 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+8 x \right ) y^{\prime }+4 y = 0 \]

1244

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

1245

\[ {}\left (3 x^{2}+x +1\right ) y^{\prime \prime }+\left (2+15 x \right ) y^{\prime }+12 y = 0 \]

1246

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

1247

\[ {}\left (x^{2}+3 x +3\right ) y^{\prime \prime }+\left (6+4 x \right ) y^{\prime }+2 y = 0 \]

1248

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

1249

\[ {}\left (2 x^{2}-3 x +2\right ) y^{\prime \prime }-\left (4-6 x \right ) y^{\prime }+2 y = 0 \]

1250

\[ {}\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y = 0 \]

1251

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

1252

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

1253

\[ {}x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y = 0 \]

1254

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

1255

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

1256

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

1257

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

1258

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

1259

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

1260

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

1261

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

1262

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

1263

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

1264

\[ {}\left (10-2 x \right ) y^{\prime \prime }+\left (1+x \right ) y = 0 \]

1265

\[ {}\left (7+x \right ) y^{\prime \prime }+\left (8+2 x \right ) y^{\prime }+\left (5+x \right ) y = 0 \]

1266

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

1267

\[ {}\left (\beta \,x^{2}+\alpha x +1\right ) y^{\prime \prime }+\left (\delta x +\gamma \right ) y^{\prime }+\epsilon y = 0 \]

1268

\[ {}\left (2 x^{2}+3 x +1\right ) y^{\prime \prime }+\left (6+8 x \right ) y^{\prime }+4 y = 0 \]

1269

\[ {}\left (6 x^{2}-5 x +1\right ) y^{\prime \prime }-\left (10-24 x \right ) y^{\prime }+12 y = 0 \]

1270

\[ {}\left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y = 0 \]

1271

\[ {}\left (x^{2}+4 x +4\right ) y^{\prime \prime }+\left (8+4 x \right ) y^{\prime }+2 y = 0 \]

1272

\[ {}\left (3 x^{2}+8 x +4\right ) y^{\prime \prime }+\left (16+12 x \right ) y^{\prime }+6 y = 0 \]

1273

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

1274

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

1275

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

1276

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

1277

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

1278

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

1279

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

1280

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

1281

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

1282

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

1283

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

1284

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

1285

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

1286

\[ {}y^{\prime \prime }+\left (3 x^{2}+12 x +13\right ) y^{\prime }+\left (5+2 x \right ) y = 0 \]

1287

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

1288

\[ {}\left (x^{2}+4 x +3\right ) y^{\prime \prime }-\left (-x^{2}+4 x +5\right ) y^{\prime }-\left (2+x \right ) y = 0 \]

1289

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

1290

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

1291

\[ {}\left (2 x^{2}-11 x +16\right ) y^{\prime \prime }+\left (x^{2}-6 x +10\right ) y^{\prime }-\left (2-x \right ) y = 0 \]

1292

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

1293

\[ {}x^{2} \left (x +3\right ) y^{\prime \prime }+5 x \left (1+x \right ) y^{\prime }-\left (1-4 x \right ) y = 0 \]

1294

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

1295

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (5 x^{2}+3 x +3\right ) y^{\prime }+y = 0 \]