4.1.36 Problems 3501 to 3600

Table 4.71: First order ode

#

ODE

Mathematica

Maple

Sympy

7060

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

7061

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

7062

\[ {} m v^{\prime } = m g -k v^{2} \]

7063

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

7064

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

7065

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

7066

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

7067

\[ {} x y^{\prime } = 4 y \]

7068

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

7069

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

7070

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

7071

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

7072

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

7073

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

7074

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

7075

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

7076

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

7077

\[ {} s^{\prime } = k s \]

7078

\[ {} q^{\prime } = k \left (q-70\right ) \]

7079

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

7080

\[ {} n^{\prime }+n = n t \,{\mathrm e}^{t +2} \]

7081

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

7082

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

7083

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

7084

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

7085

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

7086

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

7087

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

7088

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

7089

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

7090

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

7091

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

7092

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

7093

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

7094

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

7095

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

7096

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

7097

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

7098

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

7099

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

7100

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

7101

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

7102

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

7103

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

7104

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

7105

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

7106

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

7107

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

7108

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

7109

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

7110

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

7111

\[ {} y^{\prime } = \left (-1+y\right )^{2}+\frac {1}{100} \]

7112

\[ {} y^{\prime } = \left (-1+y\right )^{2}-\frac {1}{100} \]

7113

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

7114

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

7115

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

7116

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

7117

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

7118

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

7119

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

7120

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

7121

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

7122

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

7123

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

7124

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

7125

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

7126

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

7127

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

7128

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

7129

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

7130

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

7131

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

7132

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

7133

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

7134

\[ {} m^{\prime } = -\frac {k}{m^{2}} \]

7135

\[ {} u^{\prime } = a \sqrt {1+u^{2}} \]

7136

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

7137

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

7138

\[ {} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \]

7139

\[ {} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \]

7140

\[ {} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \]

7141

\[ {} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \]

7142

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

7143

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

7144

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

7145

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

7146

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

7147

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

7148

\[ {} 3 y^{\prime }+12 y = 4 \]

7149

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

7150

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

7151

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

7152

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

7153

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

7154

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

7155

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

7156

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

7157

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

7158

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

7159

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