4.1.95 Problems 9401 to 9500

Table 4.189: First order ode

#

ODE

Mathematica

Maple

Sympy

23067

\[ {} x^{\prime } = \frac {x}{t} \]

23068

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

23069

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

23070

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

23071

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

23072

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

23073

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

23074

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

23075

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

23076

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

23077

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

23078

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

23079

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

23080

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

23081

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

23082

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

23083

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

23084

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

23085

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

23086

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

23087

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

23088

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

23089

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

23090

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

23091

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

23092

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

23093

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

23094

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

23095

\[ {} y^{\prime }+7 y = {\mathrm e}^{5 x} \]

23096

\[ {} y^{\prime }-6 y = {\mathrm e}^{6 t} \]

23097

\[ {} y^{\prime }-6 y = {\mathrm e}^{6 t} \]

23098

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

23099

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

23100

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

23101

\[ {} y^{\prime }-\frac {6 y}{x} = 7 x \]

23102

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

23103

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

23104

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

23105

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

23106

\[ {} p^{\prime } = 15-20 p \]

23107

\[ {} n^{\prime } = k n-b t \]

23108

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

23109

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

23110

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

23111

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

23112

\[ {} y^{\prime }+4 y = {\mathrm e}^{k x} \]

23113

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

23114

\[ {} v^{\prime } = 60 t -4 v \]

23171

\[ {} r^{\prime } = -a \sin \left (\theta \right ) \]

23172

\[ {} \frac {r^{\prime }}{r} = \tan \left (\theta \right ) \]

23173

\[ {} \left (1+\cos \left (\theta \right )\right ) r^{\prime } = -r \sin \left (\theta \right ) \]

23174

\[ {} \cot \left (\theta \right ) r^{\prime } = r+b \]

23175

\[ {} r r^{\prime } = a \]

23176

\[ {} r^{\prime } \left (1+\frac {\cos \left (\theta \right )}{2}\right )-r \sin \left (\theta \right ) = 0 \]

23177

\[ {} \sin \left (\theta \right )^{2} r^{\prime } = -b \cos \left (\theta \right ) \]

23178

\[ {} r^{\prime } = 0 \]

23179

\[ {} r^{\prime } = c \]

23180

\[ {} r^{\prime } \left (\sin \left (\theta \right )-m \cos \left (\theta \right )\right )+r \left (\cos \left (\theta \right )+m \sin \left (\theta \right )\right ) = 0 \]

23218

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

23219

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

23228

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

23229

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

23231

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

23234

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

23235

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

23236

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

23237

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

23238

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

23239

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

23240

\[ {} y^{\prime } = y^{{2}/{3}} \]

23241

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

23242

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

23243

\[ {} x^{\prime } = \frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \]

23244

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

23245

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

23246

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

23247

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

23248

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

23249

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

23250

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

23251

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

23252

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

23253

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

23254

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

23255

\[ {} p^{\prime } = a p-b p^{2} \]

23256

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

23257

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

23258

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

23259

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

23260

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

23261

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

23262

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

23263

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

23264

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

23265

\[ {} x^{\prime } = k \left (a -x\right ) \left (b -x\right ) \]

23266

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

23267

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

23268

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

23269

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

23270

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