Problems 16901 to 17000

Table 6.339: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

16901	\[ {} y^{\prime \prime }+4 y = \sin \left (t \right ) \]	✓	✓	✓

16902	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 1 \]	✓	✓	✓

16903	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = t \]	✓	✓	✓

16904	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 t} \]	✓	✓	✓

16905	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \]	✓	✓	✓

16906	\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{t} \]	✓	✓	✓

16907	\[ {} y^{\prime } = \operatorname {Heaviside}\left (t -3\right ) \]	✓	✓	✓

16908	\[ {} y^{\prime } = \operatorname {Heaviside}\left (t -3\right ) \]	✓	✓	✓

16909	\[ {} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \]	✓	✓	✓

16910	\[ {} y^{\prime \prime } = \operatorname {Heaviside}\left (t -2\right ) \]	✓	✓	✓

16911	\[ {} y^{\prime \prime }+9 y = \operatorname {Heaviside}\left (t -10\right ) \]	✓	✓	✓

16912	\[ {} y^{\prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]	✓	✓	✓

16913	\[ {} y^{\prime \prime } = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]	✓	✓	✓

16914	\[ {} y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \]	✓	✓	✓

16915	\[ {} y^{\prime } = 3 \delta \left (t -2\right ) \]	✓	✓	✓

16916	\[ {} y^{\prime } = \delta \left (t -2\right )-\delta \left (t -4\right ) \]	✓	✓	✓

16917	\[ {} y^{\prime \prime } = \delta \left (t -3\right ) \]	✓	✓	✓

16918	\[ {} y^{\prime \prime } = \delta \left (t -1\right )-\delta \left (t -4\right ) \]	✓	✓	✓

16919	\[ {} y^{\prime }+2 y = 4 \delta \left (t -1\right ) \]	✓	✓	✓

16920	\[ {} y^{\prime \prime }+y = \delta \left (t \right )+\delta \left (t -\pi \right ) \]	✓	✓	✓

16921	\[ {} y^{\prime \prime }+y = -2 \delta \left (t -\frac {\pi }{2}\right ) \]	✓	✓	✓

16922	\[ {} 3 y+y^{\prime } = \delta \left (t -2\right ) \]	✓	✓	✓

16923	\[ {} y^{\prime \prime }+3 y^{\prime } = \delta \left (t \right ) \]	✓	✓	✓

16924	\[ {} y^{\prime \prime }+3 y^{\prime } = \delta \left (t -1\right ) \]	✓	✓	✓

16925	\[ {} y^{\prime \prime }+16 y = \delta \left (t -2\right ) \]	✓	✓	✓

16926	\[ {} y^{\prime \prime }-16 y = \delta \left (t -10\right ) \]	✓	✓	✓

16927	\[ {} y^{\prime \prime }+y = \delta \left (t \right ) \]	✓	✓	✓

16928	\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \]	✓	✓	✓

16929	\[ {} y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \]	✓	✓	✓

16930	\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \]	✓	✓	✓

16931	\[ {} y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \]	✓	✓	✓

16932	\[ {} y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (t -1\right ) \]	✓	✓	✓

16933	\[ {} y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right ) \]	✓	✓	✓

16934	\[ {} y^{\prime }-2 y = 0 \]	✓	✓	✓

16935	\[ {} y^{\prime }-2 x y = 0 \]	✓	✓	✓

16936	\[ {} y^{\prime }+\frac {2 y}{2 x -1} = 0 \]	✓	✓	✓

16937	\[ {} \left (x -3\right ) y^{\prime }-2 y = 0 \]	✓	✓	✓

16938	\[ {} \left (x^{2}+1\right ) y^{\prime }-2 x y = 0 \]	✓	✓	✓

16939	\[ {} y^{\prime }+\frac {y}{x -1} = 0 \]	✓	✓	✓

16940	\[ {} y^{\prime }+\frac {y}{x -1} = 0 \]	✓	✓	✓

16941	\[ {} \left (1-x \right ) y^{\prime }-2 y = 0 \]	✓	✓	✓

16942	\[ {} \left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0 \]	✓	✓	✓

16943	\[ {} \left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0 \]	✓	✓	✓

16944	\[ {} y^{\prime } \left (1+x \right )-x y = 0 \]	✓	✓	✓

16945	\[ {} y^{\prime } \left (1+x \right )+\left (1-x \right ) y = 0 \]	✓	✓	✓

16946	\[ {} -2 y+\left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

16947	\[ {} y+x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

16948	\[ {} \left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \]	✓	✓	✓

16949	\[ {} y^{\prime \prime }-3 x^{2} y = 0 \]	✓	✓	✓

16950	\[ {} \left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y = 0 \]	✓	✓	✓

16951	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \]	✓	✓	✓

16952	\[ {} 6 y-2 x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

16953	\[ {} \left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

16954	\[ {} y^{\prime \prime }+\left (x +2\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

16955	\[ {} \left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0 \]	✓	✓	✓

16956	\[ {} y^{\prime \prime }-2 y^{\prime }-x y = 0 \]	✓	✓	✓

16957	\[ {} y^{\prime \prime }-x y^{\prime }-2 x y = 0 \]	✓	✓	✓

16958	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y = 0 \]	✓	✓	✓

16959	\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0 \]	✓	✓	✓

16960	\[ {} 4 y+y^{\prime \prime } = 0 \]	✓	✓	✓

16961	\[ {} y^{\prime \prime }-x^{2} y = 0 \]	✓	✓	✓

16962	\[ {} y^{\prime \prime }+y \,{\mathrm e}^{2 x} = 0 \]	✓	✓	✓

16963	\[ {} \sin \left (x \right ) y^{\prime \prime }-y = 0 \]	✓	✓	✓

16964	\[ {} y^{\prime \prime }+x y = \sin \left (x \right ) \]	✓	✓	✗

16965	\[ {} y^{\prime \prime }-y^{\prime } \sin \left (x \right )-x y = 0 \]	✓	✓	✓

16966	\[ {} y^{\prime \prime }-y^{2} = 0 \]	✓	✓	✗

16967	\[ {} y^{\prime }+\cos \left (y\right ) = 0 \]	✓	✓	✓

16968	\[ {} y^{\prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

16969	\[ {} y^{\prime }-y \tan \left (x \right ) = 0 \]	✓	✓	✓

16970	\[ {} \sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

16971	\[ {} \sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

16972	\[ {} \sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-\sin \left (x \right ) y = 0 \]	✓	✓	✓

16973	\[ {} {\mathrm e}^{3 x} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+\frac {2 y}{x^{2}+4} = 0 \]	✓	✓	✓

16974	\[ {} y^{\prime \prime }+\frac {\left ({\mathrm e}^{x}+1\right ) y}{-{\mathrm e}^{x}+1} = 0 \]	✓	✓	✓

16975	\[ {} \left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0 \]	✓	✓	✓

16976	\[ {} x y^{\prime \prime }+\left (-{\mathrm e}^{x}+1\right ) y = 0 \]	✓	✓	✓

16977	\[ {} \sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0 \]	✓	✓	✗

16978	\[ {} y^{\prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

16979	\[ {} y^{\prime }+y \,{\mathrm e}^{2 x} = 0 \]	✓	✓	✓

16980	\[ {} y^{\prime }+y \cos \left (x \right ) = 0 \]	✓	✓	✓

16981	\[ {} y^{\prime }+y \ln \left (x \right ) = 0 \]	✓	✓	✗

16982	\[ {} y^{\prime \prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

16983	\[ {} y^{\prime \prime }+3 x y^{\prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

16984	\[ {} x y^{\prime \prime }-3 x y^{\prime }+\sin \left (x \right ) y = 0 \]	✓	✓	✓

16985	\[ {} y^{\prime \prime }+y \ln \left (x \right ) = 0 \]	✓	✓	✓

16986	\[ {} \sqrt {x}\, y^{\prime \prime }+y = 0 \]	✓	✓	✓

16987	\[ {} y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0 \]	✓	✓	✓

16988	\[ {} y^{\prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

16989	\[ {} y^{\prime }+\sqrt {x^{2}+1}\, y = 0 \]	✓	✓	✓

16990	\[ {} \cos \left (x \right ) y^{\prime }+y = 0 \]	✓	✓	✓

16991	\[ {} y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0 \]	✓	✓	✓

16992	\[ {} y^{\prime \prime }-y \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

16993	\[ {} y^{\prime \prime }+y \cos \left (x \right ) = 0 \]	✓	✓	✓

16994	\[ {} y^{\prime \prime }+y^{\prime } \sin \left (x \right )+y \cos \left (x \right ) = 0 \]	✓	✓	✓

16995	\[ {} \sqrt {x}\, y^{\prime \prime }+y^{\prime }+x y = 0 \]	✓	✓	✓

16996	\[ {} \left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

16997	\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \]	✓	✓	✓

16998	\[ {} \left (x -1\right )^{2} y^{\prime \prime }-5 \left (x -1\right ) y^{\prime }+9 y = 0 \]	✓	✓	✗

16999	\[ {} \left (x +2\right )^{2} y^{\prime \prime }+\left (x +2\right ) y^{\prime } = 0 \]	✓	✓	✗

17000	\[ {} 3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0 \]	✓	✓	✓

6.170 Problems 16901 to 17000