4.4.9 Problems 801 to 900

Table 4.561: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

6123

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

6124

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

6125

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

6126

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

6127

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

6129

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

6131

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

6133

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

6134

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

6135

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

6136

\[ {} \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x \left (\operatorname {a0} +x \right ) y^{\prime \prime } = 0 \]

6137

\[ {} 6 y-4 \left (x +a \right ) y^{\prime }+\left (\operatorname {a0} +x \right )^{2} y^{\prime \prime } = 0 \]

6139

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

6140

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

6141

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

6143

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

6144

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

6145

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

6146

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

6147

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

6148

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

6149

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

6150

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

6151

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

6152

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

6153

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

6154

\[ {} 12 y+2 \left (3-4 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime } = 0 \]

6155

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

6157

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

6159

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

6160

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

6161

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

6163

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

6164

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

6165

\[ {} 5 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime } = 0 \]

6166

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

6167

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

6168

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

6169

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

6170

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

6171

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

6172

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

6174

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

6175

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

6176

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

6177

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

6178

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

6179

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

6180

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

6182

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

6183

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

6184

\[ {} -\left (4 x +5\right ) y+32 x y^{\prime }+16 x^{2} y^{\prime \prime } = 0 \]

6185

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

6186

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

6187

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

6188

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

6189

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

6190

\[ {} 2 \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime } = 0 \]

6191

\[ {} \operatorname {a2} y+\operatorname {a1} \left (b x +a \right ) y^{\prime }+\left (b x +a \right )^{2} y^{\prime \prime } = 0 \]

6193

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

6194

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

6195

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

6196

\[ {} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{3} y^{\prime \prime } = 0 \]

6197

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

6198

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

6200

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

6201

\[ {} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0 \]

6202

\[ {} \operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0 \]

6203

\[ {} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0 \]

6204

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

6205

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

6207

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

6208

\[ {} 4 x y-\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]

6209

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

6210

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

6211

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

6212

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

6213

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

6214

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

6215

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

6216

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

6217

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

6218

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

6219

\[ {} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x \left (x^{2}+\operatorname {a0} \right ) y^{\prime \prime } = 0 \]

6220

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

6221

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

6222

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

6223

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

6224

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

6225

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

6226

\[ {} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0 \]

6227

\[ {} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} \left (\operatorname {a0} +x \right ) y^{\prime \prime } = 0 \]

6228

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

6229

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

6230

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

6231

\[ {} \operatorname {a0} \operatorname {a1} \left (-k +x \right ) y+\left (1-\operatorname {a0} +\operatorname {a1} +\operatorname {a0} \operatorname {a2} -\operatorname {a3} +\left (\operatorname {a2} +\operatorname {a3} \right ) x +\left (1+\operatorname {a0} +\operatorname {a1} \right ) x^{2}\right ) y^{\prime }+\left (1-x \right ) \left (a -x \right ) x y^{\prime \prime } = 0 \]

6232

\[ {} \left (\operatorname {c1} x +\operatorname {c0} \right ) y+\left (\operatorname {b2} \,x^{2}+\operatorname {b1} x +\operatorname {b0} \right ) y^{\prime }+\left (\operatorname {a1} -x \right ) \left (\operatorname {a2} -x \right ) \left (\operatorname {a3} -x \right ) y^{\prime \prime } = 0 \]

6233

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

6234

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

6235

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