4.1.102 Problems 10101 to 10200

Table 4.203: First order ode

#

ODE

Mathematica

Maple

Sympy

25046

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

25047

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

25048

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

25049

\[ {} y^{\prime } = {\mathrm e}^{2 t}-1 \]

25050

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

25052

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

25053

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

25054

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

25055

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

25056

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

25057

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

25058

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

25059

\[ {} y^{\prime } = t y^{2} \]

25060

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

25061

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

25062

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

25063

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

25064

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

25065

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

25066

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

25067

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

25068

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

25069

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

25070

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

25071

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

25072

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

25073

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

25074

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

25075

\[ {} 1-y^{2}-t y y^{\prime } = 0 \]

25076

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

25077

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

25078

\[ {} y^{\prime } = t y^{2} \]

25079

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

25080

\[ {} y^{\prime } = t^{m} y^{n} \]

25081

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

25082

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

25083

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

25084

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

25085

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

25086

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

25087

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

25088

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

25089

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

25090

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

25091

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

25092

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

25093

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

25094

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

25095

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

25096

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

25097

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

25098

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

25099

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

25100

\[ {} t y^{\prime }+m y = t \ln \left (t \right ) \]

25101

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

25102

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

25103

\[ {} y^{\prime }-3 y = 25 \cos \left (4 t \right ) \]

25104

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

25105

\[ {} z^{\prime } = 2 t \left (z-t^{2}\right ) \]

25106

\[ {} y^{\prime }+a y = b \]

25107

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

25108

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

25109

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

25110

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

25111

\[ {} y^{\prime }+a y = {\mathrm e}^{b t} \]

25112

\[ {} y^{\prime }+a y = t^{n} {\mathrm e}^{-a t} \]

25113

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

25114

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

25115

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

25116

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

25117

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

25118

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

25119

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

25120

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

25121

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

25122

\[ {} y^{\prime } = \frac {y^{2}-4 t y+6 t^{2}}{t^{2}} \]

25123

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

25124

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

25125

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

25126

\[ {} t y^{\prime } = y+\sqrt {t^{2}-y^{2}} \]

25127

\[ {} t^{2} y^{\prime } = t y+y \sqrt {t^{2}+y^{2}} \]

25128

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

25129

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

25130

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

25131

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

25132

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

25133

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

25134

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

25135

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

25136

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

25137

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

25138

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

25139

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

25140

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

25141

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

25142

\[ {} y^{\prime } = \tan \left (y\right )+\frac {2 \cos \left (t \right )}{\cos \left (y\right )} \]

25143

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

25144

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

25145

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

25146

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