3.9.6 Problems 501 to 600

Table 3.517: First order ode linear in derivative

#

ODE

Mathematica

Maple

1061

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

1062

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

1063

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

1064

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

1065

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

1066

\[ {}5 x y+2 y+5+2 x y^{\prime } = 0 \]

1067

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

1068

\[ {}27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0 \]

1069

\[ {}6 x y^{2}+2 y+\left (12 x^{2} y+12 x y^{2}\right ) y^{\prime } = 0 \]

1070

\[ {}y^{2}+\left (x y^{2}+6 x y+\frac {1}{y}\right ) y^{\prime } = 0 \]

1071

\[ {}12 x^{3} y+24 y^{2} x^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime } = 0 \]

1072

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

1073

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

1074

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

1075

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

1076

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

1077

\[ {}a y+b x y+\left (c x +d x y\right ) y^{\prime } = 0 \]

1078

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

1079

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

1080

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

1081

\[ {}x^{4} y^{4}+x^{5} y^{3} y^{\prime } = 0 \]

1082

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

1083

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

1084

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

1085

\[ {}12 x y+6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime } = 0 \]

1086

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

1142

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

1143

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

1144

\[ {}y^{\prime }+y^{2}+5 y-6 = 0 \]

1145

\[ {}y^{\prime }+y^{2}+8 y+7 = 0 \]

1146

\[ {}y^{\prime }+y^{2}+14 y+50 = 0 \]

1147

\[ {}6 y^{\prime }+6 y^{2}-y-1 = 0 \]

1148

\[ {}36 y^{\prime }+36 y^{2}-12 y+1 = 0 \]

1149

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

1150

\[ {}y^{\prime }+y^{2}+4 x y+4 x^{2}+2 = 0 \]

1151

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

1152

\[ {}\left (3 x -1\right ) \left (y^{\prime }+y^{2}\right )-\left (2+3 x \right ) y-6 x +8 = 0 \]

1153

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

1154

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

1644

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

1645

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

1646

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

1647

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

1648

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

1649

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

1650

\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \]

1651

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

1652

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

1653

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

1654

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

1655

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

1656

\[ {}\sqrt {t^{2}+1}\, y+y^{\prime } = 0 \]

1657

\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \]

1658

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

1659

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

1660

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

1661

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

1662

\[ {}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{\frac {5}{2}} \]

1663

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

1664

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

1665

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

1666

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

1667

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

1668

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

1669

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

1670

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

1671

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

1672

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

1673

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

1674

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

1675

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

1676

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

1677

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

1678

\[ {}y^{\prime } = k \left (a -y\right ) \left (b -y\right ) \]

1679

\[ {}3 t y^{\prime } = \cos \left (t \right ) y \]

1680

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

1681

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

1682

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

1683

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

1684

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

1685

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

1686

\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

1687

\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \]

1688

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

1689

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

1690

\[ {}\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0 \]

1691

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

1692

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

1693

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

1694

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

1695

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

1696

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

1697

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

1698

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

1699

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

1700

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

1701

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

1702

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

1703

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

1704

\[ {}y^{\prime } = y^{3}+{\mathrm e}^{-5 t} \]