4.1.64 Problems 6301 to 6400

Table 4.127: First order ode

#

ODE

Mathematica

Maple

Sympy

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

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

15154

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

15155

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

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

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

15161

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

15162

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

15163

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

15164

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

15165

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

15166

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

15167

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

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

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

15178

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

15179

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

15180

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

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

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

15248

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

15249

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

15250

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

15256

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

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

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

15442

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

15443

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

15444

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

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

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

15469

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

15470

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

15471

\[ {} 3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime } = 0 \]

15472

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

15473

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

15474

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

15475

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

15476

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

15477

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

15478

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

15479

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

15480

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

15481

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

15482

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

15483

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

15484

\[ {} y^{\prime }+\frac {n y}{x} = a \,x^{-n} \]

15485

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

15486

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

15487

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

15488

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

15489

\[ {} 3 y^{2} y^{\prime }-a y^{3}-x -1 = 0 \]

15490

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