4.9.55 Problems 5401 to 5500

Table 4.947: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

15007

\[ {} i^{\prime } = p \left (t \right ) i \]

15008

\[ {} x^{\prime } = \lambda x \]

15009

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

15010

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

15011

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

15012

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

15013

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

15014

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

15015

\[ {} y^{\prime }+y \,{\mathrm e}^{-x} = 1 \]

15016

\[ {} x^{\prime }+x \tanh \left (t \right ) = 3 \]

15017

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

15018

\[ {} x^{\prime }+5 x = t \]

15019

\[ {} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b \]

15020

\[ {} T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \]

15021

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

15022

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

15023

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

15024

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

15025

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

15026

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

15027

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

15028

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

15029

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

15030

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

15129

\[ {} \tan \left (y\right )-\cot \left (x \right ) y^{\prime } = 0 \]

15130

\[ {} 12 x +6 y-9+\left (5 x +2 y-3\right ) y^{\prime } = 0 \]

15131

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

15132

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

15133

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

15134

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

15135

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

15136

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

15137

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

15138

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

15141

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

15143

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

15145

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

15148

\[ {} y^{\prime } = \frac {2 y-x -4}{2 x -y+5} \]

15149

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

15150

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

15151

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

15152

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

15153

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

15156

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

15157

\[ {} y^{\prime } = \left (x -5 y\right )^{{1}/{3}}+2 \]

15158

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

15159

\[ {} x^{\prime }+5 x = 10 t +2 \]

15160

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

15163

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

15164

\[ {} x^{\prime }-x \cot \left (t \right ) = 4 \sin \left (t \right ) \]

15166

\[ {} y^{\prime }-\frac {3 y}{x}+y^{2} x^{3} = 0 \]

15168

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

15169

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

15170

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

15171

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

15172

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

15173

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

15174

\[ {} \left (3+2 x +4 y\right ) y^{\prime }-2 y-x -1 = 0 \]

15175

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

15176

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

15177

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

15229

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

15230

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

15231

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

15232

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

15233

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

15234

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

15235

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

15236

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

15237

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

15238

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

15245

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

15247

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

15249

\[ {} 5 y^{\prime }-x y = 0 \]

15334

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

15338

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

15340

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

15341

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

15361

\[ {} 10 Q^{\prime }+100 Q = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right ) \]

15441

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

15449

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

15450

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

15451

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

15452

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

15453

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

15454

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

15455

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

15456

\[ {} 1+s^{2}-\sqrt {t}\, s^{\prime } = 0 \]

15457

\[ {} r^{\prime }+r \tan \left (t \right ) = 0 \]

15458

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

15459

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

15460

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

15461

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

15462

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

15463

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

15464

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

15465

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

15466

\[ {} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

15467

\[ {} 2 \sqrt {s t}-s+t s^{\prime } = 0 \]

15468

\[ {} t -s+t s^{\prime } = 0 \]