2.21 Problems 2001 to 2100

Table 2.41: Main lookup table

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ODE

Mathematica result

Maple result

2001

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

2002

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

2003

\[ {}\sin \left (\theta \right ) r^{\prime }+1+r \tan \left (\theta \right ) = \cos \left (\theta \right ) \]

2004

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

2005

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

2006

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

2007

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

2008

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

2009

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

2010

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

2011

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

2012

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

2013

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

2014

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

2015

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

2016

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

2017

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

2018

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

2019

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

2020

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

2021

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

2022

\[ {}r^{\prime }+\left (r-\frac {1}{r}\right ) \theta = 0 \]

2023

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

2024

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

2025

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

2026

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

2027

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

2028

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

2029

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

2030

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

2031

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

2032

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

2033

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

2034

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

2035

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

2036

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

2037

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

2038

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

2039

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

2040

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

2041

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

2042

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

2043

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

2044

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

2045

\[ {}\tan \left (y\right ) = \left (4+3 x \right ) y^{\prime } \]

2046

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

2047

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

2048

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

2049

\[ {}r^{\prime } = r \cot \left (\theta \right ) \]

2050

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

2051

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

2052

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

2053

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

2054

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

2055

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

2056

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

2057

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

2058

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

2059

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

2060

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

2061

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

2062

\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right ) = \left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime } \]

2063

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

2064

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

2065

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

2066

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

2067

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

2068

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

2069

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

2070

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

2071

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

2072

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

2073

\[ {}x y^{\prime }-2 y-2 x^{4} y^{3} = 0 \]

2074

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

2075

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

2076

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

2077

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

2078

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

2079

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

2080

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

2081

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

2082

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

2083

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

2084

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

2085

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

2086

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

2087

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

2088

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

2089

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 0 \]

2090

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

2091

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = 0 \]

2092

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

2093

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

2094

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

2095

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

2096

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

2097

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

2098

\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

2099

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

2100

\[ {}y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y = 0 \]