5.9.56 Problems 5501 to 5600

Table 5.739: First order ode linear in derivative

#

ODE

Mathematica

Maple

14464

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

14465

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

14466

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

14467

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

14468

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

14469

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

14470

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

14471

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

14472

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

14473

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

14474

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

14475

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

14476

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

14477

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

14478

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

14479

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

14509

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

14521

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

14523

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

14528

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

14529

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

14535

\[ {}y^{\prime }-2 y = 6 \]

14536

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

14543

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

14550

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

14551

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

14601

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

14602

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

14603

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

14604

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

14605

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

14606

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

14607

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

14608

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

14609

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

14610

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

14611

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

14612

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

14613

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

14614

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

14615

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

14616

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

14617

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

14618

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

14619

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

14620

\[ {}w^{\prime } = \frac {w}{t} \]

14621

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

14622

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

14623

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

14624

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

14625

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

14626

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

14627

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

14628

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

14629

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

14630

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

14631

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

14632

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

14633

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

14634

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

14635

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

14636

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

14637

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

14638

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

14639

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

14640

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

14641

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

14642

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

14643

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

14644

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

14645

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

14646

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

14647

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

14648

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

14649

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

14650

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

14651

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

14652

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

14653

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

14654

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

14655

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

14656

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

14657

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

14658

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

14659

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

14660

\[ {}\theta ^{\prime } = 2 \]

14661

\[ {}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \]

14662

\[ {}v^{\prime } = -\frac {v}{R C} \]

14663

\[ {}v^{\prime } = \frac {K -v}{R C} \]

14664

\[ {}v^{\prime } = 2 V \left (t \right )-2 v \]

14665

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

14666

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

14667

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

14668

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

14669

\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \]

14670

\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \]

14671

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

14672

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

14673

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

14674

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