4.9.27 Problems 2601 to 2700

Table 4.891: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

7243

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

7244

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

7245

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

7246

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

7247

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

7248

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

7249

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

7250

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

7251

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

7252

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

7253

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

7254

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

7255

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

7256

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

7257

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

7258

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

7259

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

7260

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

7261

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

7262

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

7263

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

7264

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

7265

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

7266

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

7267

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

7268

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

7269

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

7343

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

7344

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

7347

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

7349

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

7351

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

7352

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

7353

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

7359

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

7360

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

7361

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

7363

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

7365

\[ {} \sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2} = r \cos \left (\theta \right )^{2} \]

7367

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

7368

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

7372

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

7374

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

7376

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

7391

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

7392

\[ {} y^{\prime } = 4 y^{2}-3 y+1 \]

7393

\[ {} s^{\prime } = t \ln \left (s^{2 t}\right )+8 t^{2} \]

7394

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

7395

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

7396

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

7397

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

7398

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

7399

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

7400

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

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

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