Problems 501 to 600

Table 4.825: Third and higher order linear ODE


#	ODE	Mathematica	Maple	Sympy

7529	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 4 \,{\mathrm e}^{t} \]	✓	✓	✓

7530	\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \]	✓	✓	✓

7531	\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y = g \left (t \right ) \]	✓	✓	✓

7532	\[ {} y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t} = 0 \]	✓	✓	✓

7534	\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-4 y = f \left (x \right ) \]	✓	✓	✓

7539	\[ {} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]	✓	✓	✓

7554	\[ {} a^{2} y^{\prime \prime \prime \prime } = y^{\prime \prime } \]	✓	✓	✓

7582	\[ {} y^{\prime \prime \prime } = x^{2} \]	✓	✓	✓

7640	\[ {} y^{\prime \prime \prime }-8 y = 0 \]	✓	✓	✓

7641	\[ {} y^{\prime \prime \prime \prime }+16 y = 0 \]	✓	✓	✓

7642	\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+6 y^{\prime } = 0 \]	✓	✓	✓

7643	\[ {} y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y = 0 \]	✓	✓	✓

7644	\[ {} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

7645	\[ {} y^{\prime \prime \prime \prime }-16 y = 0 \]	✓	✓	✓

7646	\[ {} y^{\prime \prime \prime }-3 y^{\prime }-2 y = 0 \]	✓	✓	✓

7647	\[ {} y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y = 0 \]	✓	✓	✓

7648	\[ {} y^{\prime \prime \prime }-4 y^{\prime } = 0 \]	✓	✓	✓

7649	\[ {} y^{\left (5\right )}-y^{\prime \prime \prime \prime }-y^{\prime }+y = 0 \]	✓	✓	✓

7652	\[ {} y^{\prime \prime \prime \prime }-y = 0 \]	✓	✓	✓

7653	\[ {} y^{\left (5\right )}+2 y = 0 \]	✓	✓	✓

7654	\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

7655	\[ {} y^{\prime \prime \prime }+y = 0 \]	✓	✓	✓

7656	\[ {} y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y = 0 \]	✓	✓	✓

7658	\[ {} y^{\prime \prime \prime \prime }-k^{4} y = 0 \]	✓	✓	✓

7659	\[ {} y^{\prime \prime \prime }-y = x \]	✓	✓	✓

7660	\[ {} y^{\prime \prime \prime }-8 y = {\mathrm e}^{i x} \]	✓	✓	✓

7661	\[ {} y^{\prime \prime \prime \prime }+16 y = \cos \left (x \right ) \]	✓	✓	✓

7662	\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y = {\mathrm e}^{x} \]	✓	✓	✓

7663	\[ {} y^{\prime \prime \prime \prime }-y = \cos \left (x \right ) \]	✓	✓	✓

7672	\[ {} y^{\prime \prime \prime } = x^{2}+{\mathrm e}^{-x} \sin \left (x \right ) \]	✓	✓	✓

7673	\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \]	✓	✓	✓

7683	\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0 \]	✓	✓	✓

7695	\[ {} y^{\prime \prime \prime }-x y = 0 \]	✓	✓	✗

7703	\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]	✓	✓	✓

7806	\[ {} 2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0 \]	✓	✓	✓

7984	\[ {} y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right ) \]	✓	✓	✓

8016	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \]	✓	✓	✓

8017	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \]	✓	✓	✓

8018	\[ {} y^{\prime \prime \prime }-y = 0 \]	✓	✓	✓

8019	\[ {} y^{\prime \prime \prime }+y = 0 \]	✓	✓	✓

8020	\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0 \]	✓	✓	✓

8021	\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0 \]	✓	✓	✓

8022	\[ {} y^{\prime \prime \prime \prime }-y = 0 \]	✓	✓	✓

8023	\[ {} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

8024	\[ {} y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y = 0 \]	✓	✓	✓

8025	\[ {} y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0 \]	✓	✓	✓

8026	\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = 0 \]	✓	✓	✓

8027	\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0 \]	✓	✓	✓

8028	\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \]	✓	✓	✓

8029	\[ {} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0 \]	✓	✓	✓

8030	\[ {} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0 \]	✓	✓	✓

8031	\[ {} y^{\prime \prime \prime \prime } = 0 \]	✓	✓	✓

8032	\[ {} y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \]	✓	✓	✓

8033	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \]	✓	✓	✓

8034	\[ {} y^{\prime \prime \prime }-y^{\prime } = 1 \]	✓	✓	✓

8035	\[ {} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0 \]	✓	✓	✓

8036	\[ {} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \]	✓	✓	✓

8037	\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]	✓	✓	✓

8038	\[ {} x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0 \]	✓	✓	✓

8332	\[ {} 2 y^{\prime \prime \prime }+3 y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{-t} \]	✓	✓	✓

8333	\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y = \sin \left (3 t \right ) \]	✓	✓	✓

8572	\[ {} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \]	✓	✓	✗

8615	\[ {} x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \]	✓	✓	✓

8858	\[ {} y^{\prime \prime \prime }-x^{3} y^{\prime }-x^{2} y-x^{3} = 0 \]	✓	✓	✗

8872	\[ {} y^{\prime \prime \prime }+y^{\prime }+y = x \]	✓	✓	✗

8876	\[ {} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+y^{\prime } x^{2}+x y = 0 \]	✓	✓	✓

8877	\[ {} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+y^{\prime } x^{2}+x y = x \]	✓	✓	✓

8878	\[ {} 5 x^{5} y^{\prime \prime \prime \prime }+4 x^{4} y^{\prime \prime \prime }+y^{\prime } x^{2}+x y = 0 \]	✓	✓	✓

9165	\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+5 y^{\prime }-2 y = {\mathrm e}^{x} x +3 \,{\mathrm e}^{-2 x} \]	✓	✓	✓

9170	\[ {} y^{\prime \prime \prime }-x y = 0 \]	✓	✓	✗

11424	\[ {} y^{\prime \prime \prime }-\lambda y = 0 \]	✓	✓	✓

11425	\[ {} y^{\prime \prime \prime }+y a \,x^{3}-b x = 0 \]	✓	✓	✗

11426	\[ {} y^{\prime \prime \prime }-a \,x^{b} y = 0 \]	✓	✓	✗

11427	\[ {} y^{\prime \prime \prime }+3 y^{\prime }-4 y = 0 \]	✓	✓	✓

11428	\[ {} y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 a x} \sin \left (x \right )^{2} = 0 \]	✓	✓	✓

11429	\[ {} y^{\prime \prime \prime }+2 a x y^{\prime }+a y = 0 \]	✓	✓	✗

11430	\[ {} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+\left (a +b -1\right ) x y^{\prime }-b y a = 0 \]	✓	✓	✗

11431	\[ {} y^{\prime \prime \prime }+x^{2 c -2} y^{\prime }+\left (c -1\right ) x^{2 c -3} y = 0 \]	✓	✓	✗

11432	\[ {} y^{\prime \prime \prime }-\left (6 k^{2} \sin \left (x \right )^{2}+a \right ) y^{\prime }+b y = 0 \]	✗	✗	✗

11433	\[ {} y^{\prime \prime \prime }+2 f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y = 0 \]	✗	✗	✗

11434	\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }+10 y = 0 \]	✓	✓	✓

11435	\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }-a^{2} y^{\prime }+2 y a^{2}-\sinh \left (x \right ) = 0 \]	✓	✓	✓

11436	\[ {} y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{a x} = 0 \]	✓	✓	✓

11437	\[ {} y^{\prime \prime \prime }+\operatorname {a2} y^{\prime \prime }+\operatorname {a1} y^{\prime }+\operatorname {a0} y = 0 \]	✓	✓	✓

11438	\[ {} y^{\prime \prime \prime }-6 x y^{\prime \prime }+2 \left (4 x^{2}+2 a -1\right ) y^{\prime }-8 a x y = 0 \]	✓	✓	✗

11439	\[ {} y^{\prime \prime \prime }+3 a x y^{\prime \prime }+3 a^{2} x^{2} y^{\prime }+a^{3} x^{3} y = 0 \]	✓	✓	✗

11440	\[ {} y^{\prime \prime \prime }-\sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+y \sin \left (x \right )-\ln \left (x \right ) = 0 \]	✓	✓	✗

11441	\[ {} y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime }+f \left (x \right ) y = 0 \]	✓	✓	✗

11442	\[ {} y^{\prime \prime \prime }+f \left (x \right ) \left (x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y\right ) = 0 \]	✓	✓	✗

11443	\[ {} 4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x} = 0 \]	✓	✓	✓

11444	\[ {} x y^{\prime \prime \prime }+3 y^{\prime \prime }+x y = 0 \]	✓	✓	✗

11445	\[ {} x y^{\prime \prime \prime }+3 y^{\prime \prime }-a \,x^{2} y = 0 \]	✓	✓	✗

11446	\[ {} x y^{\prime \prime \prime }+\left (a +b \right ) y^{\prime \prime }-x y^{\prime }-a y = 0 \]	✓	✓	✗

11447	\[ {} x y^{\prime \prime \prime }-\left (x +2 v \right ) y^{\prime \prime }-\left (x -2 v -1\right ) y^{\prime }+\left (x -1\right ) y = 0 \]	✓	✓	✗

11448	\[ {} x y^{\prime \prime \prime }+\left (x^{2}-3\right ) y^{\prime \prime }+4 x y^{\prime }+2 y-f \left (x \right ) = 0 \]	✓	✓	✗

11449	\[ {} 2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+a x y-b = 0 \]	✓	✓	✗

11450	\[ {} 2 x y^{\prime \prime \prime }-4 \left (x +\nu -1\right ) y^{\prime \prime }+\left (2 x +6 \nu -5\right ) y^{\prime }+\left (1-2 \nu \right ) y = 0 \]	✓	✓	✗

11451	\[ {} 2 x y^{\prime \prime \prime }+3 \left (2 a x +k \right ) y^{\prime \prime }+6 \left (a k +b x \right ) y^{\prime }+\left (3 b k +2 c x \right ) y = 0 \]	✗	✗	✗

11452	\[ {} \left (x -2\right ) x y^{\prime \prime \prime }-x \left (x -2\right ) y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]	✓	✓	✗

11453	\[ {} \left (2 x -1\right ) y^{\prime \prime \prime }-8 x y^{\prime }+8 y = 0 \]	✓	✓	✗

4.12.6 Problems 501 to 600