Problems 501 to 600

Table 4.555: Second ODE homogeneous ODE


#	ODE	Mathematica	Maple	Sympy

5755	\[ {} a \,x^{k} y+y^{\prime \prime } = 0 \]	✓	✓	✗

5756	\[ {} \left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5757	\[ {} \left (a +b \cos \left (2 x \right )+k \cos \left (4 x \right )\right ) y+y^{\prime \prime } = 0 \]	✗	✓	✗

5758	\[ {} y^{\prime \prime } = 2 \csc \left (x \right )^{2} y \]	✓	✓	✗

5759	\[ {} a \csc \left (x \right )^{2} y+y^{\prime \prime } = 0 \]	✓	✓	✗

5760	\[ {} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0 \]	✗	✓	✗

5761	\[ {} y^{\prime \prime } = \left (a^{2}+\left (-1+p \right ) p \csc \left (x \right )^{2}+\left (-1+q \right ) q \sec \left (x \right )^{2}\right ) y \]	✓	✓	✗

5762	\[ {} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5763	\[ {} y^{\prime \prime } = \left (1+2 \tan \left (x \right )^{2}\right ) y \]	✓	✓	✗

5764	\[ {} -\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5765	\[ {} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5766	\[ {} \left (a +b \,{\mathrm e}^{x}+c \,{\mathrm e}^{2 x}\right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5767	\[ {} a \,{\mathrm e}^{b x} y+y^{\prime \prime } = 0 \]	✓	✓	✗

5768	\[ {} \left (a +b \cosh \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5769	\[ {} \left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5770	\[ {} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0 \]	✓	✓	✗

5771	\[ {} \frac {\left (a +b \right ) y}{x^{2}}+y^{\prime \prime } = 0 \]	✓	✓	✓

5772	\[ {} x y-y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5773	\[ {} y+2 y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5781	\[ {} 3 y+2 y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5783	\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]	✓	✓	✓

5785	\[ {} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5787	\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 0 \]	✓	✓	✓

5792	\[ {} -4 y-3 y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5794	\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5796	\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5798	\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]	✓	✓	✓

5799	\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 0 \]	✓	✓	✓

5802	\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]	✓	✓	✓

5804	\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5806	\[ {} 16 y+8 y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5808	\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5810	\[ {} y b^{2}+2 a y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5813	\[ {} \left (a^{2}+b^{2}\right )^{2} y-4 a b y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5814	\[ {} b y+a y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5816	\[ {} \left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5817	\[ {} \left (c \,x^{2}+b \right ) y+a y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5818	\[ {} \left (b +{\mathrm e}^{x} c \right ) y+a y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5819	\[ {} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5820	\[ {} b \,{\mathrm e}^{k x} y+a y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5821	\[ {} y+x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5822	\[ {} -y+x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5823	\[ {} 2 y-x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5824	\[ {} n y-x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5825	\[ {} -a y-x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5826	\[ {} -\left (1-x \right ) y-x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5827	\[ {} 6 y-2 x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5828	\[ {} -8 y+2 x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5829	\[ {} 2 n y-2 x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5830	\[ {} -\left (-x^{2}-x +1\right ) y-\left (2 x +1\right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5831	\[ {} 2 \left (2 x^{2}+1\right ) y+4 x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5832	\[ {} -\left (-4 x^{2}+3\right ) y-4 x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5834	\[ {} a^{2} x^{2} y-2 a x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5835	\[ {} b y+a x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5836	\[ {} c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5837	\[ {} \left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5838	\[ {} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5839	\[ {} -2 a \left (-2 x^{2} a +1\right ) y-4 a x y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5840	\[ {} x y-x^{2} y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5842	\[ {} -4 x y+x^{2} y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5843	\[ {} -x^{3} y+x^{4} y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5844	\[ {} a \left (1+k \right ) x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0 \]	✗	✓	✗

5845	\[ {} a k \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5846	\[ {} -a \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5847	\[ {} b \,x^{k -1} y+a \,x^{k} y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5848	\[ {} 2 y-\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5849	\[ {} k \left (1+k \right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5850	\[ {} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5851	\[ {} \left (p \left (p +1\right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5852	\[ {} \left (\operatorname {a0} -\operatorname {a2} \csc \left (x \right )^{2}+4 \operatorname {a1} \sin \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5853	\[ {} 3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5855	\[ {} \left (b +k^{2} \cos \left (x \right )^{2}\right ) y+a \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✗	✓	✗

5856	\[ {} \left (a \cot \left (x \right )^{2}+b \cot \left (x \right ) \csc \left (x \right )+c \csc \left (x \right )^{2}\right ) y+k \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5857	\[ {} 2 y-\cot \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5858	\[ {} a \tan \left (x \right )^{2} y-2 \cot \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5859	\[ {} c y+a \cot \left (b x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✗	✓	✗

5860	\[ {} \left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5861	\[ {} a \tan \left (\frac {x}{2}\right )^{2} y-\csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✗	✗

5863	\[ {} \csc \left (x \right )^{2} \left (2+\sin \left (x \right )^{2}\right ) y-\csc \left (2 x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5864	\[ {} a \csc \left (x \right )^{2} y+\left (2+\cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5865	\[ {} -2 \left (\cos \left (x \right )+1\right ) \sec \left (x \right ) y-\left (2+3 \cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5866	\[ {} \sin \left (x \right )^{2} y-\left (\cot \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5868	\[ {} b \tan \left (x \right )^{2} y-2 \csc \left (2 x \right ) \left (1-a \sin \left (x \right )^{2}\right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5869	\[ {} a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5870	\[ {} a \cot \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5871	\[ {} -a \left (a +1\right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5872	\[ {} \left (a \cos \left (x \right )^{2}-\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5873	\[ {} -y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5875	\[ {} 3 y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5876	\[ {} b y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5877	\[ {} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5879	\[ {} b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5880	\[ {} y \,{\mathrm e}^{2 x}-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5881	\[ {} \left (\operatorname {a0} -\operatorname {a2} \operatorname {csch}\left (x \right )^{2}+4 \operatorname {a1} \sinh \left (x \right )^{2}\right ) y+\coth \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✗	✓	✗

5882	\[ {} \left (\operatorname {a0} +4 \operatorname {a1} \cosh \left (x \right )^{2}-\operatorname {a2} \operatorname {sech}\left (x \right )^{2}\right ) y+\tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✗	✓	✗

5883	\[ {} b y+2 \tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5884	\[ {} b y+a \tanh \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✗

5885	\[ {} f \left (x \right ) y^{\prime }+y^{\prime \prime } = 0 \]	✓	✓	✓

5886	\[ {} a k \,x^{k -1} y+2 a \,x^{k} y^{\prime }+2 y^{\prime \prime } = 0 \]	✓	✓	✗

5887	\[ {} 3 y-10 y^{\prime }+3 y^{\prime \prime } = 0 \]	✓	✓	✓

4.4.6 Problems 501 to 600