Problems 5901 to 6000

Table 6.119: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

5901	\[ {} \left (1+x^{2}+y^{2}\right ) y^{\prime }+2 x y+x^{2}+3 = 0 \]	✓	✓	✗

5902	\[ {} \cos \left (x \right ) y^{\prime }+y+\cos \left (x \right ) \left (\sin \left (x \right )+1\right ) = 0 \]	✓	✓	✓

5903	\[ {} y^{2}+12 x^{2} y+\left (2 x y+4 x^{3}\right ) y^{\prime } = 0 \]	✓	✓	✓

5904	\[ {} \left (x^{2}-y\right ) y^{\prime }+x = 0 \]	✓	✓	✓

5905	\[ {} \left (x^{2}-y\right ) y^{\prime }-4 x y = 0 \]	✓	✓	✓

5906	\[ {} x y y^{\prime }+x^{2}+y^{2} = 0 \]	✓	✓	✓

5907	\[ {} 2 x y y^{\prime }+3 x^{2}-y^{2} = 0 \]	✓	✓	✓

5908	\[ {} \left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4} = 0 \]	✓	✓	✓

5909	\[ {} \left (x y-1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0 \]	✓	✓	✓

5910	\[ {} \left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (y+2 x \right ) = 0 \]	✓	✓	✗

5911	\[ {} 3 x y^{2} y^{\prime }+y^{3}-2 x = 0 \]	✓	✓	✓

5912	\[ {} 2 y^{3} y^{\prime }+x y^{2}-x^{3} = 0 \]	✓	✓	✗

5913	\[ {} \left (2 x y^{3}+x y+x^{2}\right ) y^{\prime }-x y+y^{2} = 0 \]	✓	✓	✗

5914	\[ {} \left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0 \]	✓	✓	✓

5915	\[ {} y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0 \]	✓	✓	✓

5916	\[ {} y^{\prime \prime }+2 y^{\prime } = 0 \]	✓	✓	✓

5917	\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]	✓	✓	✓

5918	\[ {} y^{\prime \prime }-y = 0 \]	✓	✓	✓

5919	\[ {} 6 y^{\prime \prime }-11 y^{\prime }+4 y = 0 \]	✓	✓	✓

5920	\[ {} y^{\prime \prime }+2 y^{\prime }-y = 0 \]	✓	✓	✓

5921	\[ {} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0 \]	✓	✓	✓

5922	\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-4 y^{\prime \prime }+4 y^{\prime } = 0 \]	✓	✓	✓

5923	\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-2 y = 0 \]	✓	✓	✓

5924	\[ {} y^{\prime \prime \prime \prime }-y a^{2} = 0 \]	✓	✓	✓

5925	\[ {} y^{\prime \prime }-2 k y^{\prime }-2 y = 0 \]	✓	✓	✓

5926	\[ {} y^{\prime \prime }+4 k y^{\prime }-12 k^{2} y = 0 \]	✓	✓	✓

5927	\[ {} y^{\prime \prime \prime \prime } = 0 \]	✓	✓	✓

5928	\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]	✓	✓	✓

5929	\[ {} 3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \]	✓	✓	✓

5930	\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]	✓	✓	✓

5931	\[ {} y^{\prime \prime }-2 a y^{\prime }+y a^{2} = 0 \]	✓	✓	✓

5932	\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime } = 0 \]	✓	✓	✓

5933	\[ {} y^{\prime \prime \prime \prime }-2 y^{\prime \prime } = 0 \]	✓	✓	✓

5934	\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]	✓	✓	✓

5935	\[ {} 36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]	✓	✓	✓

5936	\[ {} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0 \]	✓	✓	✓

5937	\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]	✓	✓	✓

5938	\[ {} y^{\prime \prime }-y^{\prime }+y = 0 \]	✓	✓	✓

5939	\[ {} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y = 0 \]	✓	✓	✓

5940	\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]	✓	✓	✓

5941	\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

5942	\[ {} y^{\prime \prime \prime }+8 y = 0 \]	✓	✓	✓

5943	\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 0 \]	✓	✓	✓

5944	\[ {} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime } = 0 \]	✓	✓	✓

5945	\[ {} y^{\prime \prime } = 0 \]	✓	✓	✓

5946	\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]	✓	✓	✓

5947	\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]	✓	✓	✓

5948	\[ {} y^{\prime \prime }-4 y^{\prime }+20 y = 0 \]	✓	✓	✓

5949	\[ {} 3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y = 0 \]	✓	✓	✓

5950	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 4 \]	✓	✓	✓

5951	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]	✓	✓	✓

5952	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{i x} \]	✓	✓	✓

5953	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (x \right ) \]	✓	✓	✓

5954	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (x \right ) \]	✓	✓	✓

5955	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \]	✓	✓	✓

5956	\[ {} y^{\prime \prime }+y^{\prime }+y = x^{2} \]	✓	✓	✓

5957	\[ {} y^{\prime \prime }-2 y^{\prime }-8 y = 9 \,{\mathrm e}^{x} x +10 \,{\mathrm e}^{-x} \]	✓	✓	✓

5958	\[ {} y^{\prime \prime }-3 y^{\prime } = 2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \]	✓	✓	✓

5959	\[ {} y^{\prime \prime }+y^{\prime } = x^{2}+2 x \]	✓	✓	✓

5960	\[ {} y^{\prime \prime }+y^{\prime } = x +\sin \left (2 x \right ) \]	✓	✓	✓

5961	\[ {} y^{\prime \prime }+y = 4 x \sin \left (x \right ) \]	✓	✓	✓

5962	\[ {} y^{\prime \prime }+4 y = \sin \left (2 x \right ) x \]	✓	✓	✓

5963	\[ {} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \]	✓	✓	✓

5964	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-2 x}+x^{2} \]	✓	✓	✓

5965	\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{-x} \]	✓	✓	✓

5966	\[ {} y^{\prime \prime }+y^{\prime }-6 y = x +{\mathrm e}^{2 x} \]	✓	✓	✓

5967	\[ {} y^{\prime \prime }+y = \sin \left (x \right )+{\mathrm e}^{-x} \]	✓	✓	✓

5968	\[ {} y^{\prime \prime }+y = \sin \left (x \right )^{2} \]	✓	✓	✓

5969	\[ {} y^{\prime \prime }+y = \sin \left (2 x \right ) \sin \left (x \right ) \]	✓	✓	✓

5970	\[ {} y^{\prime \prime }-5 y^{\prime }-6 y = {\mathrm e}^{3 x} \]	✓	✓	✓

5971	\[ {} y^{\prime \prime }-y^{\prime }-2 y = 5 \sin \left (x \right ) \]	✓	✓	✓

5972	\[ {} y^{\prime \prime }+9 y = 8 \cos \left (x \right ) \]	✓	✓	✓

5973	\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{x} \left (2 x -3\right ) \]	✓	✓	✓

5974	\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \]	✓	✓	✓

5975	\[ {} y^{\prime \prime }+y = \sec \left (x \right ) \]	✓	✓	✓

5976	\[ {} y^{\prime \prime }+y = \cot \left (x \right ) \]	✓	✓	✓

5977	\[ {} y^{\prime \prime }+y = \sec \left (x \right )^{2} \]	✓	✓	✓

5978	\[ {} y^{\prime \prime }-y = \sin \left (x \right )^{2} \]	✓	✓	✓

5979	\[ {} y^{\prime \prime }+y = \sin \left (x \right )^{2} \]	✓	✓	✓

5980	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 \,{\mathrm e}^{x} \]	✓	✓	✓

5981	\[ {} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \]	✓	✓	✓

5982	\[ {} y^{\prime \prime }+y = 4 x \sin \left (x \right ) \]	✓	✓	✓

5983	\[ {} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \]	✓	✓	✓

5984	\[ {} y^{\prime \prime }+y = \csc \left (x \right ) \]	✓	✓	✓

5985	\[ {} y^{\prime \prime }+y = \tan \left (x \right )^{2} \]	✓	✓	✓

5986	\[ {} y^{\prime \prime }+2 y^{\prime }+y = \frac {{\mathrm e}^{-x}}{x} \]	✓	✓	✓

5987	\[ {} y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \]	✓	✓	✓

5988	\[ {} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \ln \left (x \right ) \]	✓	✓	✓

5989	\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{-x}\right ) \]	✓	✓	✓

5990	\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+y = x \]	✓	✓	✓

5991	\[ {} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right ) \]	✓	✓	✓

5992	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3} \]	✓	✓	✓

5993	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x} \]	✓	✓	✓

5994	\[ {} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x} \]	✓	✓	✓

5995	\[ {} y^{\prime \prime } = 2 y y^{\prime } \]	✓	✓	✗

5996	\[ {} y^{3} y^{\prime \prime } = k \]	✓	✓	✓

5997	\[ {} y y^{\prime \prime } = {y^{\prime }}^{2}-1 \]	✓	✓	✗

5998	\[ {} x^{2} y^{\prime \prime }+x y^{\prime } = 1 \]	✓	✓	✓

5999	\[ {} x y^{\prime \prime }-y^{\prime } = x^{2} \]	✓	✓	✓

6000	\[ {} \left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2} \]	✓	✓	✗

6.60 Problems 5901 to 6000