4.1.15 Problems 1401 to 1500

Table 4.29: First order ode

#

ODE

Mathematica

Maple

Sympy

3975

\[ {} y^{\prime }+4 y = 3 \delta \left (t -1\right ) \]

3976

\[ {} y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \]

4077

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

4078

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

4079

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

4080

\[ {} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \]

4081

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

4082

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

4083

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

4084

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

4085

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

4086

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

4087

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

4088

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

4089

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

4090

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

4091

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

4092

\[ {} y^{\prime } = 1-x^{5}+\sqrt {x} \]

4093

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

4094

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

4095

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

4096

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

4097

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

4098

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

4099

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

4100

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

4101

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

4102

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

4103

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

4104

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

4105

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

4106

\[ {} y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \]

4107

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

4108

\[ {} y^{\prime } = x +\frac {1}{x} \]

4109

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

4110

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

4111

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

4112

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

4113

\[ {} y^{\prime } = \frac {3 x -y+1}{3 y-x +5} \]

4114

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

4115

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

4116

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

4117

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

4190

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

4191

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

4192

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

4193

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

4194

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

4195

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

4196

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

4197

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

4198

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

4199

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

4200

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

4201

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

4202

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

4203

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

4204

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

4205

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

4206

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

4207

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

4208

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

4209

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

4210

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

4211

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

4212

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

4213

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

4214

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

4215

\[ {} y^{\prime } = {\mathrm e}^{y} \sin \left (x \right ) \]

4216

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

4217

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

4218

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

4219

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

4220

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

4221

\[ {} y^{\prime } = \frac {4 x y}{x^{2}+1} \]

4222

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

4223

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

4224

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

4225

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

4226

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

4227

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

4228

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

4229

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

4230

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

4231

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

4232

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

4233

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

4234

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

4235

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

4236

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

4237

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

4238

\[ {} y y^{\prime } x = \sqrt {y^{2}-9} \]

4239

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

4240

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

4241

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

4242

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

4243

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

4244

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

4245

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

4246

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