5.1.23 Problems 2201 to 2300

Table 5.45: First order ode

#

ODE

Mathematica

Maple

5116

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

5117

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

5118

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

5119

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

5120

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

5121

\[ {}x \left (a +y\right ) y^{\prime } = y \left (B x +A \right ) \]

5122

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

5123

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

5124

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

5125

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

5126

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

5127

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

5128

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

5129

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

5130

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

5131

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

5132

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

5133

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

5134

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

5135

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

5136

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

5137

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

5138

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

5139

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

5140

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

5141

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

5142

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

5143

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

5144

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

5145

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

5146

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

5147

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

5148

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

5149

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

5150

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

5151

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

5152

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

5153

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

5154

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

5155

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

5156

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

5157

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

5158

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

5159

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

5160

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

5161

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

5162

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

5163

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

5164

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

5165

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

5166

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

5167

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

5168

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

5169

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

5170

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

5171

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

5172

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

5173

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

5174

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

5175

\[ {}3 x^{2} y y^{\prime }+1+2 x y^{2} = 0 \]

5176

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

5177

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

5178

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

5179

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

5180

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

5181

\[ {}8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4} = 0 \]

5182

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

5183

\[ {}3 x^{4} y y^{\prime } = 1-2 y^{2} x^{3} \]

5184

\[ {}x^{7} y y^{\prime } = 2 x^{2}+2+5 x^{3} y \]

5185

\[ {}y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0 \]

5186

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

5187

\[ {}\left (\operatorname {g0} \left (x \right )+y \operatorname {g1} \left (x \right )\right ) y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3} \]

5188

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

5189

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

5190

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

5191

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

5192

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

5193

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

5194

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

5195

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

5196

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

5197

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

5198

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

5199

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

5200

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

5201

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

5202

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

5203

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

5204

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

5205

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

5206

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

5207

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

5208

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

5209

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

5210

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

5211

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

5212

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

5213

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

5214

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

5215

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