4.9.62 Problems 6101 to 6200

Table 4.961: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

16484

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

16485

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

16486

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

16487

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

16488

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

16489

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

16490

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

16491

\[ {} y^{\prime } = \tan \left (6 x +3 y+1\right )-2 \]

16492

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

16493

\[ {} y^{\prime } = x \left (6 y+{\mathrm e}^{x^{2}}\right ) \]

16494

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

16495

\[ {} x^{2} y^{\prime }+3 x y = 6 \,{\mathrm e}^{-x^{2}} \]

16553

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

16872

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

16873

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

16874

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

16907

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

16908

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

16912

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

16915

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

16916

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

16919

\[ {} y^{\prime }+2 y = 4 \delta \left (t -1\right ) \]

16922

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

17069

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

17075

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

17076

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

17077

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

17078

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

17079

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

17089

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

17090

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

17091

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

17092

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

17093

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

17094

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

17095

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

17096

\[ {} y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]

17097

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

17098

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

17099

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

17100

\[ {} y^{\prime } = \frac {-2 x -10}{\left (x +2\right ) \left (x -4\right )} \]

17101

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

17102

\[ {} y^{\prime } = \frac {\sqrt {x^{2}-16}}{x} \]

17103

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

17104

\[ {} y^{\prime } = \frac {1}{x^{2}-16} \]

17105

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

17106

\[ {} y^{\prime } = \sin \left (x \right )^{3} \tan \left (x \right ) \]

17107

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

17108

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

17115

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

17116

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

17117

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

17118

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

17119

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

17120

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

17121

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

17124

\[ {} 4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0 \]

17125

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

17129

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

17130

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

17137

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

17138

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

17139

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

17140

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

17141

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

17142

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

17143

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

17146

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

17147

\[ {} y^{\prime } = \frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \]

17148

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

17149

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

17150

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

17151

\[ {} y^{\prime } = y^{{1}/{5}} \]

17152

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

17153

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

17154

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

17155

\[ {} y^{\prime } = 6 y^{{2}/{3}} \]

17156

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

17157

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

17158

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

17159

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

17160

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

17161

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

17162

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

17163

\[ {} y^{\prime } = \sqrt {25-y^{2}} \]

17164

\[ {} y^{\prime } = \sqrt {25-y^{2}} \]

17165

\[ {} y^{\prime } = \sqrt {25-y^{2}} \]

17166

\[ {} y^{\prime } = \sqrt {25-y^{2}} \]

17167

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

17168

\[ {} t^{3} y^{\prime }+t^{4} y = 2 t^{3} \]

17169

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

17170

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

17171

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

17172

\[ {} \left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y = \frac {1}{t +2} \]

17173

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

17174

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

17175

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

17176

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

17177

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

17178

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