6.101 Problems 10001 to 10100

Table 6.201: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

10001

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

10002

\[ {} y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \]

10003

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

10004

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

10005

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

10006

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

10007

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

10008

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

10009

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

10010

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

10011

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

10012

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

10013

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

10014

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

10015

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

10016

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

10017

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

10018

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

10019

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

10020

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

10021

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

10022

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

10023

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

10024

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

10025

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

10026

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

10027

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

10028

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

10029

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

10030

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

10031

\[ {} p^{\prime } = a p-b p^{2} \]

10032

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

10033

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

10034

\[ {} x y^{\prime }-2 y+b y^{2} = c \,x^{4} \]

10035

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

10036

\[ {} u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}} \]

10037

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

10038

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

10039

\[ {} 5 y^{\prime \prime }+2 y^{\prime }+4 y = 0 \]

10040

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

10041

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

10042

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

10043

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

10044

\[ {} f^{\prime } = \frac {1}{f} \]

10045

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

10046

\[ {} \left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0 \]

10047

\[ {} t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0 \]

10048

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

10049

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

10050

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

10051

\[ {} t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0 \]

10052

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

10053

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

10054

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

10055

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

10056

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

10057

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

10058

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

10059

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

10060

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

10061

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

10062

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

10063

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

10064

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

10065

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

10066

\[ {} a y y^{\prime \prime }+b y = c \]

10067

\[ {} a y^{2} y^{\prime \prime }+b y^{2} = c \]

10068

\[ {} a y y^{\prime \prime }+b y = 0 \]

10069

\[ {} [x^{\prime }\left (t \right ) = 9 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )] \]

10070

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )] \]

10071

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

10072

\[ {} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )] \]

10073

\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )] \]

10074

\[ {} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+4 z \left (t \right )] \]

10075

\[ {} x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \]

10076

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

10077

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

10078

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

10079

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

10080

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

10081

\[ {} z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

10082

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

10083

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

10084

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

10085

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

10086

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

10087

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

10088

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

10089

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

10090

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

10091

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

10092

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

10093

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

10094

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

10095

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

10096

\[ {} y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0 \]

10097

\[ {} y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0 \]

10098

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

10099

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

10100

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