4.9.33 Problems 3201 to 3300

Table 4.903: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

8415

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

8416

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

8417

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

8419

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

8420

\[ {} m^{\prime } = -\frac {k}{m^{2}} \]

8421

\[ {} u^{\prime } = a \sqrt {1+u^{2}} \]

8422

\[ {} x^{\prime } = k \left (A -x\right )^{2} \]

8424

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8425

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8426

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8427

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8428

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

8429

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

8430

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

8431

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

8432

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

8433

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

8434

\[ {} 3 y^{\prime }+12 y = 4 \]

8435

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

8436

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

8437

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

8438

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

8439

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

8440

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

8441

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

8442

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

8443

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

8444

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

8445

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

8446

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

8447

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

8448

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

8449

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

8450

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

8451

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

8452

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

8453

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

8454

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

8455

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

8456

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

8457

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

8458

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

8459

\[ {} L i^{\prime }+R i = E \]

8460

\[ {} T^{\prime } = k \left (T-T_{m} \right ) \]

8461

\[ {} x y^{\prime }+y = 1+4 x \]

8462

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

8463

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

8464

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

8465

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

8466

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

8467

\[ {} 2 y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \]

8468

\[ {} y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \]

8469

\[ {} y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \]

8470

\[ {} \left (x^{2}+1\right ) y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \]

8471

\[ {} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y = 4 x \]

8472

\[ {} y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y = 0 \]

8473

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

8474

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

8475

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

8476

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

8477

\[ {} 2 x^{2} y+x^{3} y^{\prime } = 10 \sin \left (x \right ) \]

8478

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

8479

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

8480

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

8481

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

8482

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

8483

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

8485

\[ {} e^{\prime } = -\frac {e}{r c} \]

8486

\[ {} 2 x -1+\left (3 y+7\right ) y^{\prime } = 0 \]

8633

\[ {} y^{\prime }+\frac {26 y}{5} = \frac {97 \sin \left (2 t \right )}{5} \]

8634

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

8645

\[ {} y^{\prime }-6 y = 0 \]

8668

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

8669

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

8670

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

8671

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

8672

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

8673

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

8674

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

8675

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

8676

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

8677

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

8678

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

8679

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

8680

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

8681

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

8682

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

8683

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

8684

\[ {} \frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}} = 0 \]

8685

\[ {} \frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}} = 0 \]

8686

\[ {} 2 x \sqrt {1-y^{2}}+y y^{\prime } = 0 \]

8687

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

8688

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

8689

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

8690

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

8691

\[ {} z^{\prime } = 10^{x +z} \]

8692

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

8693

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

8694

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

8695

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