4.1.103 Problems 10201 to 10252

Table 4.205: First order ode

#

ODE

Mathematica

Maple

Sympy

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

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