6.75 Problems 7401 to 7500

Table 6.149: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

7401

\[ {} x v^{\prime } = \frac {1-4 v^{2}}{3 v} \]

7402

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

7403

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

7404

\[ {} x^{\prime }-x^{3} = x \]

7405

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

7406

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

7407

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

7408

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

7409

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

7410

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

7411

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

7412

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

7413

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

7414

\[ {} y^{\prime } = 8 x^{3} {\mathrm e}^{-2 y} \]

7415

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

7416

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

7417

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

7418

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

7419

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

7420

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

7421

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

7422

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

7423

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

7424

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

7425

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

7426

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

7427

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

7428

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

7429

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

7430

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

7431

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

7432

\[ {} 3 t = {\mathrm e}^{t} y^{\prime }+y \ln \left (t \right ) \]

7433

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

7434

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

7435

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

7436

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

7437

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

7438

\[ {} x y^{\prime }+2 y = \frac {1}{x^{3}} \]

7439

\[ {} t +y+1-y^{\prime } = 0 \]

7440

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

7441

\[ {} y x^{\prime }+2 x = 5 y^{3} \]

7442

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

7443

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

7444

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

7445

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

7446

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

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

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