4.9.28 Problems 2701 to 2800

Table 4.893: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

7447

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

7448

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

7449

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

7450

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

7451

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

7452

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

7453

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

7454

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

7455

\[ {} x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \]

7456

\[ {} u^{\prime } = \alpha \left (1-u\right )-\beta u \]

7457

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

7458

\[ {} x^{{10}/{3}}-2 y+x y^{\prime } = 0 \]

7459

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

7460

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

7461

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

7462

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

7463

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

7464

\[ {} \theta r^{\prime }+3 r-\theta -1 = 0 \]

7465

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

7466

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

7467

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

7468

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

7469

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

7470

\[ {} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0 \]

7471

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

7472

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

7473

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

7474

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

7475

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

7476

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

7477

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

7478

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

7479

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

7480

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

7481

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

7482

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

7483

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

7484

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

7485

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

7486

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

7487

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

7488

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

7489

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

7490

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

7491

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

7492

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

7493

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

7494

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

7495

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

7496

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

7497

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

7498

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

7499

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

7500

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

7501

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

7502

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

7503

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

7504

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

7505

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

7506

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

7507

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

7508

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

7509

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

7510

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

7511

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

7512

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

7513

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

7514

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

7515

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

7516

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

7517

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

7518

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

7519

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

7520

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

7521

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

7522

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

7523

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

7524

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

7525

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

7526

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

7527

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

7528

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

7529

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

7530

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

7531

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

7532

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

7534

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

7535

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

7536

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

7537

\[ {} y^{\prime }-4 y = 32 x^{2} \]

7538

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

7539

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

7540

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

7541

\[ {} t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]

7542

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

7543

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

7544

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

7545

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

7546

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

7547

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