Problems 6601 to 6700

Table 6.133: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

6601	\[ {} -{y^{\prime }}^{2}+4 {y^{\prime }}^{3} y+y y^{\prime \prime } = 0 \]	✓	✓	✗

6602	\[ {} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3} \]	✓	✓	✗

6603	\[ {} {y^{\prime }}^{2} \left (1-b^{2} {y^{\prime }}^{2}\right )+2 b^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2}-b^{2} y^{2}\right ) {y^{\prime \prime }}^{2} = 0 \]	✗	✓	✗

6604	\[ {} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2} = 4 x y \left (x y^{\prime }-y\right )^{3} \]	✓	✗	✗

6605	\[ {} {y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right ) \]	✗	✓	✗

6606	\[ {} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0 \]	✓	✗	✗

6607	\[ {} f \left (y^{\prime \prime }\right )+x y^{\prime \prime } = y^{\prime } \]	✓	✓	✗

6608	\[ {} f \left (\frac {y^{\prime \prime }}{y^{\prime }}\right ) y^{\prime } = {y^{\prime }}^{2}-y y^{\prime \prime } \]	✗	✓	✗

6609	\[ {} f \left (y^{\prime \prime }, y^{\prime }-x y^{\prime \prime }, y-x y^{\prime }+\frac {x^{2} y^{\prime \prime }}{2}\right ) = 0 \]	✗	✓	✗

6610	\[ {} y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6611	\[ {} y^{\prime \prime \prime } = \cos \left (x \right )+1 \]	✓	✓	✓

6612	\[ {} \sin \left (x \right )+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6613	\[ {} y^{\prime \prime \prime } = \sin \left (x \right )^{3} \]	✓	✓	✓

6614	\[ {} y^{\prime \prime \prime } = y \]	✓	✓	✓

6615	\[ {} y^{\prime \prime \prime } = y+x^{2} \]	✓	✓	✓

6616	\[ {} y^{\prime \prime \prime } = x \,{\mathrm e}^{x}+\cos \left (x \right )^{2}+y \]	✓	✓	✓

6617	\[ {} a y+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6618	\[ {} y^{\prime \prime \prime } = x y \]	✓	✓	✗

6619	\[ {} y^{\prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6620	\[ {} y^{\prime \prime \prime } = y^{\prime } \]	✓	✓	✓

6621	\[ {} y^{\prime }+y^{\prime \prime \prime } = x^{3}+\cos \left (x \right ) \]	✓	✓	✓

6622	\[ {} 4 y-2 y^{\prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6623	\[ {} 4 y-2 y^{\prime }+y^{\prime \prime \prime } = {\mathrm e}^{x} \cos \left (x \right ) \]	✓	✓	✓

6624	\[ {} 2 y-3 y^{\prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6625	\[ {} 2 y-3 y^{\prime }+y^{\prime \prime \prime } = 3 \,{\mathrm e}^{x} \]	✓	✓	✓

6626	\[ {} 2 y-3 y^{\prime }+y^{\prime \prime \prime } = x^{2} {\mathrm e}^{x} \]	✓	✓	✓

6627	\[ {} -4 y^{\prime }+y^{\prime \prime \prime } = -3 \,{\mathrm e}^{2 x}+x^{2} \]	✓	✓	✓

6628	\[ {} y^{\prime \prime \prime }-7 y^{\prime }+6 y = 0 \]	✓	✓	✓

6629	\[ {} y^{\prime \prime \prime } = a^{2} y \]	✓	✓	✓

6630	\[ {} y+2 x y^{\prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6631	\[ {} a y+2 a x y^{\prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6632	\[ {} f^{\prime }\left (x \right ) y+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime } = 0 \]	✗	✗	✗

6633	\[ {} y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6634	\[ {} y+y^{\prime }-y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6635	\[ {} -3 y+y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6636	\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 0 \]	✓	✓	✓

6637	\[ {} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = {\mathrm e}^{-x} \]	✓	✓	✓

6638	\[ {} 4 y+4 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6639	\[ {} 4 y+2 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime } = \sin \left (2 x \right ) \]	✓	✓	✓

6640	\[ {} -15 y-7 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6641	\[ {} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6642	\[ {} y^{\prime }+2 y^{\prime \prime }+y^{\prime \prime \prime } = \left (x -1\right ) x \]	✓	✓	✓

6643	\[ {} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x} \]	✓	✓	✓

6644	\[ {} 2 y-y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = \sinh \left (x \right ) \]	✓	✓	✓

6645	\[ {} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6646	\[ {} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = 3 x^{2}+\sin \left (x \right ) \]	✓	✓	✓

6647	\[ {} -3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = {\mathrm e}^{-x}+3 x^{2} \]	✓	✓	✓

6648	\[ {} 10 y+3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6649	\[ {} 2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6650	\[ {} 2 a^{2} y-a^{2} y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = \sinh \left (x \right ) \]	✓	✓	✓

6651	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0 \]	✓	✓	✓

6652	\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = 0 \]	✓	✓	✓

6653	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = x^{2} \]	✓	✓	✓

6654	\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y = \cosh \left (x \right ) \]	✓	✓	✓

6655	\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0 \]	✓	✓	✓

6656	\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = x \,{\mathrm e}^{-x} \]	✓	✓	✓

6657	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = x \left (1-x^{2} {\mathrm e}^{x}\right ) \]	✓	✓	✓

6658	\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = \left (-x^{2}+2\right ) {\mathrm e}^{-x} \]	✓	✓	✓

6659	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \]	✓	✓	✓

6660	\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = {\mathrm e}^{x}+\cos \left (x \right ) \]	✓	✓	✓

6661	\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 0 \]	✓	✓	✓

6662	\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = x \]	✓	✓	✓

6663	\[ {} -4 y+6 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6664	\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime } = 0 \]	✓	✓	✓

6665	\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x^{2} {\mathrm e}^{2 x} \]	✓	✓	✓

6666	\[ {} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6667	\[ {} -a^{3} y+3 a^{2} y^{\prime }-3 a y^{\prime \prime }+y^{\prime \prime \prime } = {\mathrm e}^{a x} \]	✓	✓	✓

6668	\[ {} y^{\prime \prime \prime } = a y^{\prime \prime } \]	✓	✓	✓

6669	\[ {} \operatorname {a3} y+\operatorname {a2} y^{\prime }+\operatorname {a1} y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6670	\[ {} -8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 x y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6671	\[ {} a^{3} x^{3} y+3 a^{2} x^{2} y^{\prime }+3 a x y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6672	\[ {} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6673	\[ {} -y^{\prime }+\left (2 \cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime \prime }+y^{\prime \prime \prime } = \cot \left (x \right ) \]	✓	✓	✗

6674	\[ {} \sin \left (x \right ) y-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = \ln \left (x \right ) \]	✓	✓	✗

6675	\[ {} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✗	✗	✗

6676	\[ {} f \left (x \right ) y+y^{\prime }+f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6677	\[ {} 4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0 \]	✓	✓	✓

6678	\[ {} -3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6679	\[ {} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6680	\[ {} x y^{\prime \prime \prime } = 2 \]	✓	✓	✓

6681	\[ {} x y+3 y^{\prime }+x y^{\prime \prime \prime } = 0 \]	✗	✓	✗

6682	\[ {} -y+x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6683	\[ {} y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6684	\[ {} y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime } = -x^{2}+1 \]	✓	✓	✗

6685	\[ {} -x^{2} y+3 y^{\prime \prime }+x y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6686	\[ {} 2 y+4 x y^{\prime }-\left (-x^{2}+3\right ) y^{\prime \prime }+x y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6687	\[ {} -2 y^{\prime }-\left (x +4\right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6688	\[ {} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6689	\[ {} 2 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = a \]	✓	✓	✓

6690	\[ {} 3 x y+y^{\prime } \left (x^{2}+2\right )+4 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = f \left (x \right ) \]	✓	✓	✗

6691	\[ {} 4 y^{\prime }+5 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = \ln \left (x \right ) \]	✓	✓	✓

6692	\[ {} 6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6693	\[ {} a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6694	\[ {} 6 n y^{\prime }-2 \left (n +1\right ) x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6695	\[ {} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0 \]	✗	✗	✗

6696	\[ {} 10 y^{\prime }+8 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]	✗	✓	✗

6697	\[ {} -2 x y+y^{\prime } \left (x^{2}+2\right )-2 x y^{\prime \prime }+\left (x^{2}+2\right ) y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6698	\[ {} -2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime } = 0 \]	✓	✓	✗

6699	\[ {} y^{\prime }+\left (x +2\right ) y^{\prime \prime }+\left (x +2\right )^{2} y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6700	\[ {} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime } = 0 \]	✓	✓	✓

6.67 Problems 6601 to 6700