Problems 15901 to 16000

Table 6.319: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

15901	\[ {} y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x \]	✓	✓	✓

15902	\[ {} y^{\prime }+2 \cot \left (x \right ) y = \cos \left (x \right ) \]	✓	✓	✓

15903	\[ {} y^{\prime }+x y = x^{3} \]	✓	✓	✓

15904	\[ {} y^{\prime }-x y = x \]	✓	✓	✓

15905	\[ {} y^{\prime } = \frac {1}{x +y^{2}} \]	✓	✓	✓

15906	\[ {} y^{\prime }-x = y \]	✓	✓	✓

15907	\[ {} y-\left (x +3 y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

15908	\[ {} x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1} \]	✓	✓	✓

15909	\[ {} p^{\prime } = t^{3}+\frac {p}{t} \]	✓	✓	✓

15910	\[ {} v^{\prime }+v = {\mathrm e}^{-s} \]	✓	✓	✓

15911	\[ {} y^{\prime }-y = 4 \,{\mathrm e}^{t} \]	✓	✓	✓

15912	\[ {} y^{\prime }+y = {\mathrm e}^{-t} \]	✓	✓	✓

15913	\[ {} y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}} \]	✓	✓	✓

15914	\[ {} y^{\prime }+2 t y = 2 t \]	✓	✓	✓

15915	\[ {} t y^{\prime }+y = \cos \left (t \right ) \]	✓	✓	✓

15916	\[ {} t y^{\prime }+y = 2 t \,{\mathrm e}^{t} \]	✓	✓	✓

15917	\[ {} \left (1+{\mathrm e}^{t}\right ) y^{\prime }+{\mathrm e}^{t} y = t \]	✓	✓	✓

15918	\[ {} \left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t \]	✓	✓	✓

15919	\[ {} x^{\prime } = x+t +1 \]	✓	✓	✓

15920	\[ {} y^{\prime } = {\mathrm e}^{2 t}+2 y \]	✓	✓	✓

15921	\[ {} y^{\prime }-\frac {y}{t} = \ln \left (t \right ) \]	✓	✓	✓

15922	\[ {} y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t} \]	✓	✓	✓

15923	\[ {} y^{\prime }+y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \]	✓	✓	✗

15924	\[ {} y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \]	✓	✓	✗

15925	\[ {} y^{\prime }-y = \sin \left (2 t \right ) \]	✓	✓	✓

15926	\[ {} y^{\prime }+y = 5 \,{\mathrm e}^{2 t} \]	✓	✓	✓

15927	\[ {} y^{\prime }+y = {\mathrm e}^{-t} \]	✓	✓	✓

15928	\[ {} y^{\prime }+y = 2-{\mathrm e}^{2 t} \]	✓	✓	✓

15929	\[ {} y^{\prime }-5 y = t \]	✓	✓	✓

15930	\[ {} y^{\prime }+3 y = 27 t^{2}+9 \]	✓	✓	✓

15931	\[ {} y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \]	✓	✓	✓

15932	\[ {} y^{\prime }+4 y = 8 \cos \left (4 t \right ) \]	✓	✓	✓

15933	\[ {} y^{\prime }+10 y = 2 \,{\mathrm e}^{t} \]	✓	✓	✓

15934	\[ {} y^{\prime }-3 y = 27 t^{2} \]	✓	✓	✓

15935	\[ {} y^{\prime }-y = 2 \,{\mathrm e}^{t} \]	✓	✓	✓

15936	\[ {} y^{\prime }+y = 4+3 \,{\mathrm e}^{t} \]	✓	✓	✓

15937	\[ {} y^{\prime }+y = 2 \cos \left (t \right )+t \]	✓	✓	✓

15938	\[ {} y^{\prime }+\frac {y}{2} = \sin \left (t \right ) \]	✓	✓	✓

15939	\[ {} y^{\prime }-\frac {y}{2} = \sin \left (t \right ) \]	✓	✓	✓

15940	\[ {} t y^{\prime }+y = t \cos \left (t \right ) \]	✓	✓	✓

15941	\[ {} y^{\prime }+y = t \]	✓	✓	✓

15942	\[ {} y^{\prime }+y = \sin \left (t \right ) \]	✓	✓	✓

15943	\[ {} y^{\prime }+y = \cos \left (t \right ) \]	✓	✓	✓

15944	\[ {} y^{\prime }+y = {\mathrm e}^{t} \]	✓	✓	✓

15945	\[ {} y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0 \]	✓	✓	✗

15946	\[ {} \frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0 \]	✓	✓	✓

15947	\[ {} y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0 \]	✓	✓	✓

15948	\[ {} y \sec \left (t \right )^{2}+2 t +\tan \left (t \right ) y^{\prime } = 0 \]	✓	✓	✗

15949	\[ {} 3 t y^{2}+y^{3} y^{\prime } = 0 \]	✓	✓	✓

15950	\[ {} t -y \sin \left (t \right )+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0 \]	✓	✓	✗

15951	\[ {} y \sin \left (2 t \right )+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0 \]	✓	✓	✗

15952	\[ {} \ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0 \]	✓	✓	✓

15953	\[ {} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \]	✓	✓	✓

15954	\[ {} 3 t^{2}-y^{\prime } = 0 \]	✓	✓	✓

15955	\[ {} -1+3 y^{2} y^{\prime } = 0 \]	✓	✓	✓

15956	\[ {} y^{2}+2 t y y^{\prime } = 0 \]	✓	✓	✓

15957	\[ {} \frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0 \]	✓	✓	✓

15958	\[ {} 2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime } = 0 \]	✓	✓	✗

15959	\[ {} -\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

15960	\[ {} 2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

15961	\[ {} 2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0 \]	✓	✓	✗

15962	\[ {} \sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

15963	\[ {} 3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \]	✓	✓	✓

15964	\[ {} {\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✓

15965	\[ {} 3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime } = 0 \]	✓	✓	✗

15966	\[ {} -2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

15967	\[ {} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

15968	\[ {} 1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0 \]	✗	✗	✗

15969	\[ {} 2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

15970	\[ {} \left (3+t \right ) \cos \left (y+t \right )+\sin \left (y+t \right )+\left (3+t \right ) \cos \left (y+t \right ) y^{\prime } = 0 \]	✓	✓	✓

15971	\[ {} \frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0 \]	✓	✓	✗

15972	\[ {} -\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0 \]	✓	✓	✓

15973	\[ {} 2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0 \]	✓	✓	✓

15974	\[ {} 2 t y^{2}+2 t^{2} y y^{\prime } = 0 \]	✓	✓	✓

15975	\[ {} 1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0 \]	✓	✓	✓

15976	\[ {} 2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0 \]	✓	✓	✓

15977	\[ {} 1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

15978	\[ {} {\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0 \]	✗	✗	✗

15979	\[ {} 2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0 \]	✓	✓	✗

15980	\[ {} y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0 \]	✓	✓	✗

15981	\[ {} \cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0 \]	✓	✓	✗

15982	\[ {} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0 \]	✗	✗	✗

15983	\[ {} \frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0 \]	✗	✗	✗

15984	\[ {} -2 x -y \cos \left (x y\right )+\left (2 y-x \cos \left (x y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

15985	\[ {} -4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

15986	\[ {} t^{2} y+t^{3} y^{\prime } = 0 \]	✓	✓	✓

15987	\[ {} y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0 \]	✓	✓	✓

15988	\[ {} y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \]	✓	✓	✓

15989	\[ {} 2 t y+y^{2}-t^{2} y^{\prime } = 0 \]	✓	✓	✓

15990	\[ {} y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime } = 0 \]	✓	✓	✓

15991	\[ {} 5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0 \]	✓	✓	✗

15992	\[ {} 5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0 \]	✓	✓	✓

15993	\[ {} 2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime } = 0 \]	✓	✓	✓

15994	\[ {} 2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

15995	\[ {} -1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime } = 0 \]	✓	✓	✗

15996	\[ {} 2 t +2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

15997	\[ {} \frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

15998	\[ {} 2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \]	✓	✓	✓

15999	\[ {} y^{\prime }-\frac {y}{2} = \frac {t}{y} \]	✓	✓	✓

16000	\[ {} y^{\prime }+y = t y^{2} \]	✓	✓	✓

6.160 Problems 15901 to 16000