Problems 8201 to 8300

Table 6.165: Main lookup table sequentially arranged


#	ODE	Mathematica	Maple	Sympy

8201	\[ {} y^{\prime } = y^{2}+2 y-3 \]	✓	✓	✓

8202	\[ {} \left (y-1\right ) y^{\prime } = 1 \]	✓	✓	✓

8203	\[ {} y^{\prime \prime }+4 y^{\prime }+6 y = 10 \]	✓	✓	✓

8204	\[ {} {y^{\prime }}^{2} = 4 y \]	✓	✓	✓

8205	\[ {} {y^{\prime }}^{2} = 9-y^{2} \]	✓	✓	✓

8206	\[ {} y y^{\prime }+\sqrt {16-y^{2}} = 0 \]	✓	✓	✓

8207	\[ {} {y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1 \]	✓	✓	✗

8208	\[ {} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right )] \]	✓	✓	✓

8209	\[ {} [x^{\prime \prime }\left (t \right ) = 4 y \left (t \right )+{\mathrm e}^{t}, y^{\prime \prime }\left (t \right ) = 4 x \left (t \right )-{\mathrm e}^{t}] \]	✓	✓	✓

8210	\[ {} y^{\prime } = \sqrt {1-y^{2}} \]	✓	✓	✓

8211	\[ {} y^{\prime \prime }+2 y^{\prime }+4 y = 5 \sin \left (t \right ) \]	✓	✓	✓

8212	\[ {} y^{\prime } = f \left (x \right ) \]	✓	✓	✓

8213	\[ {} y^{\prime \prime } = f \left (x \right ) \]	✓	✓	✓

8214	\[ {} x {y^{\prime }}^{2}-4 y^{\prime }-12 x^{3} = 0 \]	✓	✓	✓

8215	\[ {} y^{\prime } = 5-y \]	✓	✓	✓

8216	\[ {} y^{\prime } = 4+y^{2} \]	✓	✓	✓

8217	\[ {} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y = 0 \]	✓	✓	✓

8218	\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y = 0 \]	✓	✓	✓

8219	\[ {} y^{\prime } = y-y^{2} \]	✗	✓	✓

8220	\[ {} y^{\prime } = y-y^{2} \]	✗	✓	✓

8221	\[ {} y^{\prime }+2 x y^{2} = 0 \]	✓	✓	✓

8222	\[ {} y^{\prime }+2 x y^{2} = 0 \]	✓	✓	✓

8223	\[ {} y^{\prime }+2 x y^{2} = 0 \]	✓	✓	✓

8224	\[ {} y^{\prime }+2 x y^{2} = 0 \]	✓	✓	✓

8225	\[ {} x^{\prime \prime }+x = 0 \]	✓	✓	✓

8226	\[ {} x^{\prime \prime }+x = 0 \]	✓	✓	✓

8227	\[ {} x^{\prime \prime }+x = 0 \]	✓	✓	✓

8228	\[ {} x^{\prime \prime }+x = 0 \]	✓	✓	✓

8229	\[ {} -y+y^{\prime \prime } = 0 \]	✓	✓	✓

8230	\[ {} -y+y^{\prime \prime } = 0 \]	✓	✓	✓

8231	\[ {} -y+y^{\prime \prime } = 0 \]	✓	✓	✓

8232	\[ {} -y+y^{\prime \prime } = 0 \]	✓	✓	✓

8233	\[ {} y^{\prime } = 3 y^{{2}/{3}} \]	✓	✓	✓

8234	\[ {} x y^{\prime } = 2 y \]	✓	✓	✗

8235	\[ {} y^{\prime } = y^{{2}/{3}} \]	✓	✓	✓

8236	\[ {} y^{\prime } = \sqrt {x y} \]	✓	✓	✓

8237	\[ {} x y^{\prime } = y \]	✓	✓	✓

8238	\[ {} y^{\prime }-y = x \]	✓	✓	✓

8239	\[ {} \left (4-y^{2}\right ) y^{\prime } = x^{2} \]	✓	✓	✓

8240	\[ {} \left (y^{3}+1\right ) y^{\prime } = x^{2} \]	✓	✓	✓

8241	\[ {} \left (x^{2}+y^{2}\right ) y^{\prime } = y^{2} \]	✓	✓	✓

8242	\[ {} \left (y-x \right ) y^{\prime } = x +y \]	✓	✓	✓

8243	\[ {} y^{\prime } = \sqrt {y^{2}-9} \]	✓	✓	✗

8244	\[ {} y^{\prime } = \sqrt {y^{2}-9} \]	✓	✓	✓

8245	\[ {} y^{\prime } = \sqrt {y^{2}-9} \]	✓	✓	✓

8246	\[ {} y^{\prime } = \sqrt {y^{2}-9} \]	✓	✓	✗

8247	\[ {} x y^{\prime } = y \]	✓	✓	✗

8248	\[ {} y^{\prime } = 1+y^{2} \]	✗	✓	✓

8249	\[ {} y^{\prime } = y^{2} \]	✓	✓	✓

8250	\[ {} y^{\prime } = y^{2} \]	✓	✓	✓

8251	\[ {} y^{\prime } = y^{2} \]	✓	✓	✗

8252	\[ {} y^{\prime } = y^{2} \]	✓	✓	✓

8253	\[ {} y^{\prime } = y^{2} \]	✓	✓	✓

8254	\[ {} y y^{\prime } = 3 x \]	✓	✓	✓

8255	\[ {} y y^{\prime } = 3 x \]	✓	✓	✓

8256	\[ {} y y^{\prime } = 3 x \]	✓	✓	✓

8257	\[ {} 4 y+y^{\prime \prime } = 0 \]	✗	✗	✗

8258	\[ {} 4 y+y^{\prime \prime } = 0 \]	✓	✓	✓

8259	\[ {} 4 y+y^{\prime \prime } = 0 \]	✓	✓	✓

8260	\[ {} 4 y+y^{\prime \prime } = 0 \]	✓	✓	✓

8261	\[ {} 4 y+y^{\prime \prime } = 0 \]	✓	✓	✓

8262	\[ {} 4 y+y^{\prime \prime } = 0 \]	✗	✗	✗

8263	\[ {} y^{\prime } = x -2 y \]	✓	✓	✓

8264	\[ {} y^{\prime } = x^{2}+y^{2} \]	✓	✓	✗

8265	\[ {} 2 y^{\prime \prime }-3 y^{2} = 0 \]	✗	✓	✗

8266	\[ {} 2 y+y^{\prime } = 3 x -6 \]	✓	✓	✓

8267	\[ {} y^{\prime } = x \sqrt {y} \]	✓	✓	✗

8268	\[ {} x y^{\prime } = 2 x \]	✓	✓	✓

8269	\[ {} y^{\prime } = 2 \]	✓	✓	✓

8270	\[ {} y^{\prime } = 2 y-4 \]	✓	✓	✓

8271	\[ {} x y^{\prime } = y \]	✓	✓	✓

8272	\[ {} y^{\prime \prime }+9 y = 18 \]	✓	✓	✓

8273	\[ {} x y^{\prime \prime }-y^{\prime } = 0 \]	✓	✓	✓

8274	\[ {} y^{\prime \prime } = y^{\prime } \]	✓	✓	✓

8275	\[ {} y^{\prime } = y \left (y-3\right ) \]	✓	✓	✓

8276	\[ {} 3 x y^{\prime }-2 y = 0 \]	✓	✓	✓

8277	\[ {} \left (-2+2 y\right ) y^{\prime } = 2 x -1 \]	✓	✓	✓

8278	\[ {} x y^{\prime }+y = 2 x \]	✓	✓	✓

8279	\[ {} y^{\prime } = x^{2}+y^{2} \]	✓	✓	✗

8280	\[ {} {y^{\prime }}^{2} = 4 x^{2} \]	✓	✓	✓

8281	\[ {} y^{\prime } = 6 \sqrt {y}+5 x^{3} \]	✗	✗	✗

8282	\[ {} y^{\prime \prime }+y = 2 \cos \left (x \right )-2 \sin \left (x \right ) \]	✓	✓	✓

8283	\[ {} y^{\prime \prime }+y = \sec \left (x \right ) \]	✓	✓	✓

8284	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \]	✓	✓	✓

8285	\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+y = \sec \left (\ln \left (x \right )\right ) \]	✓	✓	✓

8286	\[ {} y^{\prime }+\sin \left (x \right ) y = x \]	✓	✓	✓

8287	\[ {} y^{\prime }-2 x y = {\mathrm e}^{x} \]	✓	✓	✓

8288	\[ {} x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+\left (1-x \right ) y = 0 \]	✓	✓	✗

8289	\[ {} y^{\prime \prime }+y = {\mathrm e}^{x^{2}} \]	✓	✓	✓

8290	\[ {} x y^{\prime }+y = \frac {1}{y^{2}} \]	✓	✓	✓

8291	\[ {} 1+{y^{\prime }}^{2} = \frac {1}{y^{2}} \]	✓	✓	✓

8292	\[ {} y^{\prime \prime } = 2 {y^{\prime }}^{3} y \]	✓	✓	✗

8293	\[ {} \left (1-x y\right ) y^{\prime } = y^{2} \]	✓	✓	✓

8294	\[ {} y^{\prime \prime }+9 y = 5 \]	✓	✓	✓

8295	\[ {} 2 y+y^{\prime } = 3 x \]	✓	✓	✓

8296	\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]	✓	✓	✓

8297	\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]	✓	✓	✓

8298	\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]	✓	✓	✓

8299	\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 x +4 \]	✓	✓	✓

8300	\[ {} y^{\prime } = x^{2}-y^{2} \]	✓	✓	✗

6.83 Problems 8201 to 8300