4.1.74 Problems 7301 to 7400

Table 4.147: First order ode

#

ODE

Mathematica

Maple

Sympy

17388

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

17389

\[ {} 2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0 \]

17390

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

17391

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

17392

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

17393

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

17394

\[ {} t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0 \]

17395

\[ {} y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \]

17396

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

17397

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

17398

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

17399

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

17400

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

17401

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

17402

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

17403

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

17404

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

17405

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

17406

\[ {} 1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

17407

\[ {} 5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \]

17408

\[ {} 3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0 \]

17409

\[ {} 2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0 \]

17410

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

17411

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

17412

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

17413

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

17414

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

17415

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

17416

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

17417

\[ {} y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \]

17418

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

17419

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

17420

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

17421

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

17422

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

17423

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

17424

\[ {} y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \]

17425

\[ {} \cos \left (4 x \right )-8 y^{\prime } \sin \left (y\right ) = 0 \]

17426

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

17427

\[ {} y^{\prime } = \frac {{\mathrm e}^{8 y}}{t} \]

17428

\[ {} y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \]

17429

\[ {} -\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime } \]

17430

\[ {} y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \]

17431

\[ {} y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (x -1\right ) \left (2 x -5\right )} \]

17432

\[ {} 3 y+y^{\prime } = -10 \sin \left (t \right ) \]

17433

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

17434

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

17435

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

17436

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

17437

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

17438

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

17439

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

17440

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

17441

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

17442

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

17443

\[ {} y+y^{\prime } = 5 \]

17444

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

17445

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

17446

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

17447

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

17448

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

17449

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

17450

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

17451

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

17452

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

17453

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

17454

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

17455

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

17456

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

17457

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

17458

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

17459

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

17460

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

17461

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

17462

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

17463

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

17587

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

17588

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

17589

\[ {} -y+y^{\prime } = {\mathrm e}^{4 t} \]

17590

\[ {} y^{\prime }+4 y = {\mathrm e}^{-4 t} \]

17591

\[ {} y^{\prime }+4 y = t \,{\mathrm e}^{-4 t} \]

17951

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

17952

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

17953

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

17954

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

17955

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

17956

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

17957

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

17958

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

17959

\[ {} y^{\prime } = 1-\cot \left (y\right ) \]

17960

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

17961

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

17962

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

17963

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

17964

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

17965

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

17966

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

17967

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

17968

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

17969

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