4.9.89 Problems 8801 to 8897

Table 4.1015: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

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

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

25147

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

25148

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

25149

\[ {} 3 y-5 t +2 y y^{\prime }-t y^{\prime } = 0 \]

25150

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

25151

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

25152

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

25153

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

25154

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

25155

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

25156

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

25157

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

25158

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

25159

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

25160

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

25161

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

25162

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

25163

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

25164

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

25165

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

25166

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

25167

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

25168

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

25169

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

25170

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

25171

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

25172

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

25173

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

25174

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

25175

\[ {} y^{\prime }-4 y = 0 \]

25176

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

25177

\[ {} y^{\prime }-4 y = {\mathrm e}^{4 t} \]

25178

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

25179

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

25180

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

25207

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

25404

\[ {} -y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right . \]

25405

\[ {} 3 y+y^{\prime } = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right . \]

25406

\[ {} -y+y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ -t +3 & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right . \]

25407

\[ {} y+y^{\prime } = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right . \]

25410

\[ {} y^{\prime } = \left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \]

25411

\[ {} y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right . \]

25412

\[ {} y^{\prime }+5 y = \left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right . \]

25413

\[ {} y^{\prime }-3 y = \left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right . \]

25414

\[ {} y^{\prime }+2 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]

25415

\[ {} y^{\prime }-4 y = \left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right . \]

25416

\[ {} 3 y+y^{\prime } = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

25423

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

25424

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

25425

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

25426

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

25433

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

25434

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