6.151 Problems 15001 to 15100

Table 6.301: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

15001

\[ {}y^{\prime } = 40 \,{\mathrm e}^{2 x} x \]

15002

\[ {}\left (x +6\right )^{{1}/{3}} y^{\prime } = 1 \]

15003

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

15004

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

15005

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

15006

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

15007

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

15008

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

15009

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

15010

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

15011

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

15012

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

15013

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

15014

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

15015

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

15016

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

15017

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

15018

\[ {}y^{\prime } = {\mathrm e}^{-9 x^{2}} \]

15019

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

15020

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

15021

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

15022

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

15023

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

15024

\[ {}y^{\prime }+3 x y = 6 x \]

15025

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

15026

\[ {}y^{\prime }-y^{3} = 8 \]

15027

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

15028

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

15029

\[ {}y^{3}-25 y+y^{\prime } = 0 \]

15030

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

15031

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

15032

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

15033

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

15034

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

15035

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

15036

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

15037

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

15038

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

15039

\[ {}y^{\prime }+4 y = 8 \]

15040

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

15041

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

15042

\[ {}y^{\prime } = x y-3 x -2 y+6 \]

15043

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

15044

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

15045

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

15046

\[ {}y^{\prime } = y^{2}+9 \]

15047

\[ {}x y y^{\prime } = y^{2}+9 \]

15048

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

15049

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

15050

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

15051

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

15052

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

15053

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

15054

\[ {}y y^{\prime } = 3 \sqrt {x y^{2}+9 x} \]

15055

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

15056

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

15057

\[ {}y y^{\prime } = x y^{2}-9 x \]

15058

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

15059

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

15060

\[ {}y^{\prime } = 200 y-2 y^{2} \]

15061

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

15062

\[ {}y^{\prime } = x y-3 x -2 y+6 \]

15063

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

15064

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

15065

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

15066

\[ {}y^{\prime } = \frac {6 x^{2}+4}{3 y^{2}-4 y} \]

15067

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

15068

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

15069

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

15070

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

15071

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

15072

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

15073

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

15074

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

15075

\[ {}y^{\prime } = 200 y-2 y^{2} \]

15076

\[ {}y^{\prime }-2 y = -10 \]

15077

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

15078

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

15079

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

15080

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

15081

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

15082

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

15083

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

15084

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

15085

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

15086

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

15087

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

15088

\[ {}y^{\prime } = 4 y+8 \]

15089

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

15090

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

15091

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

15092

\[ {}x y^{\prime }+\cos \left (x^{2}\right ) = 827 y \]

15093

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

15094

\[ {}y^{\prime }+2 y = 20 \,{\mathrm e}^{3 x} \]

15095

\[ {}y^{\prime } = 4 y+16 x \]

15096

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

15097

\[ {}x y^{\prime }+3 y-10 x^{2} = 0 \]

15098

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

15099

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

15100

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