Problems 6201 to 6300

Table 6.125: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

6201	\[ {} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0 \]	✓	✓	✗

6202	\[ {} \operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0 \]	✓	✓	✗

6203	\[ {} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime } = 0 \]	✓	✓	✗

6204	\[ {} 6 x y+\left (-x^{3}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

6205	\[ {} -y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

6206	\[ {} x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6207	\[ {} a \,x^{3} y-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6208	\[ {} 4 x y-\left (x^{2}+7\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6209	\[ {} 2 x y-2 \left (x^{2}+1\right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6210	\[ {} -2 x y-2 y^{\prime } \left (-x^{2}+1\right )+x \left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6211	\[ {} -2 x y-2 y^{\prime } \left (-x^{2}+1\right )+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6212	\[ {} c x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6213	\[ {} \left (a -1\right ) \left (a +b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6214	\[ {} 2 \left (1-b \right ) x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6215	\[ {} c x y+\left (a -\left (a +1\right ) x^{2}\right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6216	\[ {} c x y+\left (b \,x^{2}+a \right ) y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6217	\[ {} -6 x y-y^{\prime }+x \left (x^{2}+2\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6218	\[ {} -\left (x^{2}+4 x +2\right ) y-\left (-x^{3}-3 x^{2}+2 x +2\right ) y^{\prime }+x \left (-x^{2}+2\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6219	\[ {} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x \left (x^{2}+\operatorname {a0} \right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6220	\[ {} -\left (1+x \right )^{3} y+x y^{\prime }+x^{2} \left (1+x \right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6221	\[ {} y-x \left (1+x \right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6222	\[ {} \left (2 x +1\right ) y-x \left (2 x +1\right ) y^{\prime }+x^{2} \left (1+x \right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6223	\[ {} 2 \left (1+x \right ) y+2 \left (2-x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6224	\[ {} \left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6225	\[ {} 2 \left (3 x +1\right ) y+2 x \left (2+3 x \right ) y^{\prime }+x^{2} \left (1+x \right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6226	\[ {} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6227	\[ {} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{2} \left (\operatorname {a0} +x \right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6228	\[ {} -2 y+\left (1-x \right )^{2} x y^{\prime \prime } = 0 \]	✓	✓	✗

6229	\[ {} y+x \left (1+x \right ) y^{\prime }+x \left (x^{2}+1\right ) y^{\prime \prime } = 0 \]	✗	✓	✗

6230	\[ {} 2 y+2 \left (2-x \right ) y^{\prime }+\left (2-x \right )^{2} x y^{\prime \prime } = 0 \]	✓	✓	✗

6231	\[ {} \operatorname {a0} \operatorname {a1} \left (-k +x \right ) y+\left (1-\operatorname {a0} +\operatorname {a1} +\operatorname {a0} \operatorname {a2} -\operatorname {a3} +\left (\operatorname {a2} +\operatorname {a3} \right ) x +\left (1+\operatorname {a0} +\operatorname {a1} \right ) x^{2}\right ) y^{\prime }+\left (1-x \right ) \left (a -x \right ) x y^{\prime \prime } = 0 \]	✓	✓	✗

6232	\[ {} \left (\operatorname {c1} x +\operatorname {c0} \right ) y+\left (\operatorname {b2} \,x^{2}+\operatorname {b1} x +\operatorname {b0} \right ) y^{\prime }+\left (\operatorname {a1} -x \right ) \left (\operatorname {a2} -x \right ) \left (\operatorname {a3} -x \right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6233	\[ {} -6 x y+6 x^{2} y^{\prime }+\left (-2 x^{3}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

6234	\[ {} -\left (1+x \right ) y+\left (3-5 x \right ) x y^{\prime }+2 \left (1-x \right ) x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6235	\[ {} \left (3-x \right ) y-\left (4-x \right ) x y^{\prime }+2 \left (2-x \right ) x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6236	\[ {} -6 x y+2 y^{\prime }+x \left (3 x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6237	\[ {} \left (3 x +1\right ) y-4 x^{2} y^{\prime }+4 x^{2} \left (1+x \right ) y^{\prime \prime } = 0 \]	✓	✓	✓

6238	\[ {} 2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6239	\[ {} \left (b x +a \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime } = 0 \]	✓	✓	✗

6240	\[ {} \left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime } = 0 \]	✗	✗	✗

6241	\[ {} a^{2} y+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✓

6242	\[ {} \left (-2 x^{2}+1\right ) y+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✓

6243	\[ {} -\left (2 x^{2}+1\right ) y+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✓

6244	\[ {} \left (-a^{2}+{\mathrm e}^{\frac {2}{x}}\right ) y+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6245	\[ {} -2 y+x y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6246	\[ {} \left (2 x +1\right ) y-2 x^{2} y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6247	\[ {} y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✓

6248	\[ {} -\left (1+x \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6249	\[ {} \left (c \,x^{4}+b \,x^{2}+a \right ) y+x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✗	✓	✗

6250	\[ {} y+x \left (x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6251	\[ {} \left (-x^{2}+1\right ) y-x \left (-x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6252	\[ {} a^{2} y+2 x^{3} y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✓

6253	\[ {} -y+x \left (2 x^{2}+1\right ) y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6254	\[ {} b y+2 x^{2} \left (x +a \right ) y^{\prime }+x^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6255	\[ {} -x^{2} y-\left (-x^{3}+1\right ) y^{\prime }+x \left (x^{3}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6256	\[ {} -2 y-x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✓

6257	\[ {} \left (-x^{2}+2\right ) y-x \left (-x^{2}+2\right ) y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6258	\[ {} a \left (a +1\right ) y-2 x^{3} y^{\prime }+x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6259	\[ {} y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6260	\[ {} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6261	\[ {} -a^{2} y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✗	✓	✗

6262	\[ {} -\left (m^{2}-n \left (n +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6263	\[ {} -\left (k^{2}-p \left (p +1\right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6264	\[ {} -\left (a^{2}-k \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6265	\[ {} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6266	\[ {} b y+a x \left (-x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✗	✓	✗

6267	\[ {} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6268	\[ {} y b^{2}+x \left (a^{2}+2 x^{2}\right ) y^{\prime }+x^{2} \left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0 \]	✗	✓	✗

6269	\[ {} -\left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y+2 x \left (a^{2}+2 x^{2}\right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} y^{\prime \prime } = 0 \]	✗	✗	✗

6270	\[ {} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (a^{2}-x^{2}\right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} y^{\prime \prime } = 0 \]	✗	✓	✗

6271	\[ {} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime } = 0 \]	✗	✗	✗

6272	\[ {} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}-x^{2}\right )^{2} \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0 \]	✗	✗	✗

6273	\[ {} -2 \left (1-x \right ) y+2 \left (3-x \right ) x \left (1+x \right ) y^{\prime }+\left (1-x \right ) x \left (1+x \right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6274	\[ {} \left (c \,x^{2}+b x +a \right ) y+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6275	\[ {} -y+\left (1-2 x \right ) \left (1-x \right ) x y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6276	\[ {} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (1-x \right ) x \left (\operatorname {b2} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6277	\[ {} b y+\left (a -x \right )^{2} x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6278	\[ {} \left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = k^{2} y \]	✓	✓	✗

6279	\[ {} B y+\left (a -x \right ) \left (-x +b \right ) \left (A +2 x \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6280	\[ {} -y-2 \left (a -x \right )^{3} y^{\prime }+\left (a -x \right )^{4} y^{\prime \prime } = 0 \]	✓	✓	✓

6281	\[ {} 2 \left (3 x +1\right ) y+2 \left (2-3 x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6282	\[ {} 2 \left (1-x \right ) y+2 \left (1-2 x \right ) \left (2-x \right ) x y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) x^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6283	\[ {} -\left (4 k^{2}+\left (4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6284	\[ {} -\left (4 k^{2}+\left (-4 p^{2}+1\right ) \left (-x^{2}+1\right )\right ) y-8 x \left (-x^{2}+1\right ) y^{\prime }+4 \left (-x^{2}+1\right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6285	\[ {} -\left (a \left (a +1\right ) \left (1-x \right )+b^{2} x \right ) y+2 \left (1-3 x \right ) \left (1-x \right ) x y^{\prime }+4 x^{2} \left (-x^{2}+1\right ) y^{\prime \prime } = 0 \]	✗	✓	✗

6286	\[ {} y+\left (b x +a \right )^{4} y^{\prime \prime } = 0 \]	✓	✓	✗

6287	\[ {} A y+\left (c \,x^{2}+b x +a \right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6288	\[ {} -y+x y^{\prime }+x^{5} y^{\prime \prime } = 0 \]	✓	✓	✗

6289	\[ {} \left (-2 x^{3}+1\right ) y-x \left (-2 x^{3}+1\right ) y^{\prime }+x^{5} y^{\prime \prime } = 0 \]	✓	✓	✗

6290	\[ {} x^{3} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+\left (\operatorname {b0} \,x^{4}+\operatorname {a0} \right ) y^{\prime }+x \left (a^{2}-x^{2}\right ) \left (b^{2}-x^{2}\right ) y^{\prime \prime } = 0 \]	✗	✗	✗

6291	\[ {} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0 \]	✓	✓	✓

6292	\[ {} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0 \]	✓	✓	✓

6293	\[ {} y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime } = 0 \]	✓	✓	✗

6294	\[ {} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (-x +b \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (-x +b \right )^{2} \left (c -x \right )^{2} y^{\prime \prime } = 0 \]	✓	✓	✗

6295	\[ {} \left (-2 x^{2}+1\right ) y+4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime } = 0 \]	✓	✓	✗

6296	\[ {} \left (8 x^{4}+10 x^{2}+1\right ) y-4 x^{3} \left (2 x^{2}+1\right ) y^{\prime }+4 x^{6} y^{\prime \prime } = 0 \]	✓	✓	✗

6297	\[ {} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime } = 0 \]	✓	✓	✓

6298	\[ {} \left (1-a \right )^{2} y+a \,x^{2 a -1} y^{\prime }+x^{2 a} y^{\prime \prime } = 0 \]	✓	✓	✗

6299	\[ {} a^{2} x^{a -1} y+\left (-2 a +1\right ) x^{a} y^{\prime }+x^{a +1} y^{\prime \prime } = 0 \]	✓	✓	✗

6300	\[ {} \left (\operatorname {a2} +\operatorname {b2} \,x^{k}\right ) y+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) y^{\prime }+x^{2} \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime \prime } = 0 \]	✓	✓	✗

6.63 Problems 6201 to 6300