4.9.53 Problems 5201 to 5300

Table 4.943: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

14348

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

14349

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

14350

\[ {} x^{\prime } = 6 t \left (x-1\right )^{{2}/{3}} \]

14351

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

14352

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

14354

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

14355

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

14356

\[ {} x^{\prime } = 2 t^{3} x-6 \]

14357

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

14358

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

14359

\[ {} 7 t^{2} x^{\prime } = 3 x-2 t \]

14360

\[ {} x x^{\prime } = 1-t x \]

14362

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

14363

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

14364

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

14365

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

14366

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

14367

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

14368

\[ {} x^{\prime }+\frac {5 x}{t} = t +1 \]

14369

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

14370

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

14371

\[ {} N^{\prime } = N-9 \,{\mathrm e}^{-t} \]

14372

\[ {} \cos \left (\theta \right ) v^{\prime }+v = 3 \]

14373

\[ {} R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \]

14374

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

14375

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

14376

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

14378

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

14379

\[ {} x^{\prime } = a x+b \]

14380

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

14381

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

14382

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

14383

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

14384

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

14385

\[ {} x^{\prime } = a x+b x^{3} \]

14386

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

14387

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

14388

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

14389

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

14390

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

14391

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

14392

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

14465

\[ {} x^{\prime }+5 x = \operatorname {Heaviside}\left (t -2\right ) \]

14466

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

14474

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

14476

\[ {} x^{\prime } = x-2 \operatorname {Heaviside}\left (t -1\right ) \]

14477

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

14481

\[ {} x^{\prime }+3 x = \delta \left (t -1\right )+\operatorname {Heaviside}\left (t -4\right ) \]

14527

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

14531

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

14532

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

14533

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

14534

\[ {} y^{\prime }+4 x y = 8 x \]

14539

\[ {} 2 y+y^{\prime } = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x} \]

14543

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

14544

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

14550

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

14551

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

14552

\[ {} y^{\prime } = y^{{1}/{3}} \]

14553

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

14554

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

14555

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

14556

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

14557

\[ {} 6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0 \]

14558

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

14559

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

14560

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

14561

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

14562

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

14563

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

14564

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

14565

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

14566

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

14567

\[ {} \frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0 \]

14568

\[ {} 4 x +3 y^{2}+2 y y^{\prime } x = 0 \]

14569

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

14570

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

14571

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

14572

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

14573

\[ {} 2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0 \]

14574

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

14575

\[ {} \tan \left (\theta \right )+2 r \theta ^{\prime } = 0 \]

14576

\[ {} \left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0 \]

14577

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

14578

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

14579

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

14580

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

14581

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

14582

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

14583

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

14584

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

14585

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

14586

\[ {} 8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0 \]

14587

\[ {} \left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0 \]

14588

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

14589

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

14590

\[ {} 3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0 \]

14591

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

14592

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

14593

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